Question

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Answer 1

Solving Equations

To solve linear equations, we must perform inverse operations on both sides of the equal sign to cancel values out.

• If something is being added to x, subtract it from both sides.
• If something is being subtracted from x, add it on both sides.
• Same with multiplication and division. If x is being divided, multiply. If x is being multiplied, divide.

We perform inverse operations to combine like terms. This means to get x to one side and everything else on the other.

Solving the Questions

Question 1

$5x+7=15$

Because 7 is being added to x, subtract it from both sides:

$5x+7-7=15-7\\5x=8$

Because x is being multiplied by 5, divide both sides by 5:

$\dfrac{5x}{5}=\dfrac{8}{5}\\\\x=\dfrac{8}{5}$

Therefore. $x=\dfrac{8}{5}$.

Question 2

$7x+4=5x-18$

Here, we can group all the x values on the left side of the equation. Subtract 5x from both sides:

$7x+4-5x=5x-18-5x\\2x+4=-18$

To isolate x, subtract 4 from both sides:

$2x+4-4=-18-4\\2x=-22$

Divide both sides by 2:

$\dfrac{2x}{2}=\dfrac{-22}{2}\\\\x=-11$

Therefore, $x=-11$.