1 Answer

Divina · Answer 1 · 2023-10-14T06:59:11+0000

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.

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:

$(5x)/(5)=(8)/(5)\\\\x=(8)/(5)$

Therefore.
x=(8)/(5) .

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:

$(2x)/(2)=(-22)/(2)\\\\x=-11$

Therefore,
x=-11 .