Solving Linear Equations

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~w+7=357\\&\text{What value of }w\text{ is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x+40=95\\&\text{What value of }x\text{ is the solution to the givenequation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~k+12=336\\&\text{What is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2.6+x=2.8\\&\text{What value of }x\text{ is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(p+3)+8=10\\&\text{What value of }p\text{ is the solution to the given equation ?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4x+5=165\\&\text{What is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~20x+72=32x\\
&\text{What value of }x\text{ is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~13x=42-x\\
&\text{What value of }x\text{ is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7x-6x+130=260\\
&\text{What value of }x\text{ is the solution to the given equation?}\end{aligned}\)

\(\text{If }6n=12,\text{what is the value of }n+4?\)

\(\text{If }\frac{6}{7}p+18=54,\text{what is the value of }7p?\)

\(\text{If }2x+3=9,\text{what is the value of }4x-4?\)

\(\text{If }\frac{x}{8}=5,\text{what is the value of }\frac{8}{x}?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4x+6=18\\&\text{Which equation has the same solution as the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~16x+30=190\\&\text{Which equation has the same solution as the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7(2x-3)=63\\&\text{Which equation has the same solution as the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~9x+x=2x+x+5\\&\text{Which equation has the same solution as the given equation?}\end{aligned}\)

\(\text{Which of the following is equivalent to }4x+6=12?\)

\(\text{If }12+\frac{7(3-x)}{6}=\frac{5(3-x)}{3},\text{which equation must also be true?}\)

\(\text{If }8x=6,\text{what is the value of }72x?\)

\(\text{If }4x+2=12,\text{what is the value of }16x+8?\)

\(\text{If }4x-28=-24,\text{what is the value of }x-7?\)

\(\text{If }6+x=9,\text{what is the value of }18+3x?\)

\(\text{If }(x+9)-5=25,\text{what is the value of }x+9?\)

\(\text{If }9(x+3)=81,\text{what is the value of }x+3?\)

\(\text{If }46=16+2(x-8),\text{what is the value of }2(x-8)?\)

\(\text{If }8(x+7)=7(x+7)+68,\text{what is the value of }x+7?\)

\(\text{If }9(4-3x)+2=8(4-3x)+18,\text{what is the value of }4-3x?\)

\(\begin{aligned}&\text{If }-9(15-3x)+5=-10(15-3x)+21,\text{what is the value of }\\&15-3x?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4(x-3)=13+2(x-3)\\
&\text{If }x\text{ is the solution to the given equation, what is the value}\\&\text{of }x-3?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6(x-4)=(x-4)+6\\
&\text{If }x\text{ is the solution to the given equation, what is the value}\\&\text{of }x-4?\end{aligned}\)

\(\text{If }2(x-5)+3(x-5)=10,\text{what is the value of }x-5?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~5(y-15)+10=4(y-15)+10\\&\text{What value of }y\text{ is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~5(t+3)-7(t+3)=38\\
&\text{What value of }t\text{ is the solution to the given equation?}\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~\frac{1}{6}(x+2)-\frac{1}{5}(x+2)=-5\\&\text{What value of }x\text{ is the solution to the given equation?}\end{aligned}\)

\(\text{If }\frac{x+6}{3}=\frac{x+6}{13},\text{the value of }x+6\text{ is between which of the following pairs of values?}\)

\(\text{If }\frac{x-16}{27}=\frac{x-16}{9},\text{what is the vaue of }x+16?\)

\(\text{Which equation has no solution?}\)

\(\text{Which equation has no solution?}\)

\(\text{Which equation has no solution?}\)

\(\text{Which of the following equations has exactly one solution?}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~10x=10\\
&\text{How many solutions does the given equation have?}\\
\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~66x=66x\\
&\text{How many solutions does the given equation have?}\\
\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6x+4=6x+8\\
&\text{How many solutions does the given equation have?}\\
\end{aligned}\)

\(\text{How many solution does the equation }5x+3=5x\text{ have }?\)

\(\text{How many solution does the equation }7x-19=19-7x\text{ have }?\)

\(\text{How many solution does the equation }9x+6=5x+4x+12\text{ have }?\)

\(\text{How many solution does the equation }17(x-16)=-16(x+17)\text{ have }?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6x+k=6x+5\\&\text{In the given equation, }k\text{ is a constant. If the equation has infinitely many solutions,}\\&\text{what is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2x+16=a(x+8)\\
&\text{In the given equation, }a\text{ is a constant. If the equation has infinitely many solutions,}\\&\text{what is the value of }a?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(b-2)x=8\\&\text{In the given equation, }b\text{ is a constant. If the equation has no solution,}\\&\text{what is the value of }b?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~3(kx+13)=\frac{48}{17}x+36\\
&\text{In the given equation, }k\text{ is a constant. The equation has no solution.}\\&\text{What is the value of }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-3x+21px=84\\
&\text{In the given equation, }p\text{ is a constant. The equation has no solution.}\\
&\text{What is the value of }p?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{8(cx+3)}{5}=4x-3\\
&\text{In the given equation, }c\text{ is a constant. If the equation has no solution,}\\
&\text{what is the value of }c?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2ax-15=3(x+5)+5(x-1)\\
&\text{In the equation above, a is a constant. If no value of }x\text{ satisfies the equation, }\\
&\text{what is the value of }a?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{12x+28}{4}-\frac{s}{13}=r(x-8)\\
&\text{In the given equation, }s\text{ and }r\text{ are constants, and }s > 0\text{. If the equation has infinitely}\\&\mathrm{many~solutions,~what~is~the~value~of~}s?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-\frac{3}{19}rx+\frac{s}{8}=10-\frac{5}{57}x\\&\text{In the given equation, }r\mathrm{~and~}s\text{ are constants. The equation has no solution.}\\&\text{What is the value of }r?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a(7x-14)+5a=7(ax-2a)-35\\
&\mathrm{In~the~given~equation,~}a\text{ is a constant. The equation has infinitely many solutions.}\\
&\text{What are all possible values of }a?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a(x+b)=4x+10\\
&\text{In the equation above, }a\text{ and }b\text{ are constants. If the equation has infinitely many solutions for}\\
&x\text{ , what is the value of }b?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a(3-x)-b=-1-2x\\&\text{In the equation above, }a\mathrm{~and~}b\text{ are constants. If the equation has infinitely many}\\&\text{solutions, what are the values of }a\mathrm{~and~}b\mathrm{~?}\end{aligned}\)

\(\begin{aligned}&\text{The equation }9x+5=a(x+b)\text{, where }a\text{ and }b\text{ are constants, has no solutions.}\\
&\text{Which of the following must be true?}\\&~~\mathrm{I.~~~}a=9\\&~~\mathrm{II.~~}b=5\\&~~\mathrm{III.~}b\neq\frac{5}{9}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~c(x-6)=-7(x+k)\\
&\text{In the given equation, }c\text{ and }k\text{ are constants. The equation has exactly one solution. }\\
&\text{Which of the following statements must be true?}\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~nx+3t=-3x+4n\\&\text{In the given equation, }n\mathrm{~and~}t\text{ are constants. The equation has no solution.}\\&\text{What CANNOT be the value of }n+t?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~2\left(x+\frac{b}{2}-17\right)=2x\\
&\text{In the given equation, }b\text{ is a constant. The equation has infinitely many solutions.}\\&\text{What is the value of }b?\end{aligned}\)