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
[tex]5x+7=15[/tex]
Because 7 is being added to x, subtract it from both sides:
[tex]5x+7-7=15-7\\5x=8[/tex]
Because x is being multiplied by 5, divide both sides by 5:
[tex]\dfrac{5x}{5}=\dfrac{8}{5}\\\\x=\dfrac{8}{5}[/tex]
Therefore. [tex]x=\dfrac{8}{5}[/tex].
Question 2
[tex]7x+4=5x-18[/tex]
Here, we can group all the x values on the left side of the equation. Subtract 5x from both sides:
[tex]7x+4-5x=5x-18-5x\\2x+4=-18[/tex]
To isolate x, subtract 4 from both sides:
[tex]2x+4-4=-18-4\\2x=-22[/tex]
Divide both sides by 2:
[tex]\dfrac{2x}{2}=\dfrac{-22}{2}\\\\x=-11[/tex]
Therefore, [tex]x=-11[/tex].
