Solve 5x − 12 = −52

The solution of 5x − 12 = −52 is x = -8.

5x - 12 = -52\ \Rightarrow\ x = -8

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The lines y = 5x − 12 and y = -52 meet at x = -8. The solution of the equation is the x-coordinate of the point where the two sides are equal.

How to work it out

1
The goal is to get x alone. Undo the operations in the opposite order: first the subtraction, then the multiplication.
$5x - 12 = -52$
2
Add 12 to both sides:
$5x - 12 + 12 = -52 + 12 \ \Rightarrow\ 5x = -40$
3
Divide both sides by 5:
$\frac{5x}{5} = \frac{-40}{5} \ \Rightarrow\ x = -8$
4
Check: put x = -8 back into the equation.
$5\cdot(-8) - 12 = -40 - 12 = -52 \checkmark$

LaTeX source of the formulas on this page

\[ 5x - 12 = -52\ \Rightarrow\ x = -8 \]
\[ 5x - 12 = -52 \]
\[ 5x - 12 + 12 = -52 + 12 \ \Rightarrow\ 5x = -40 \]
\[ \frac{5x}{5} = \frac{-40}{5} \ \Rightarrow\ x = -8 \]
\[ 5\cdot(-8) - 12 = -40 - 12 = -52 \checkmark \]

Trying values of x in 5x − 12 = −52

x	5x − 12	Equals -52?
-10	-62	no
-9	-57	no
-8	-52	yes
-7	-47	no
-6	-42	no

Questions

What is x in 5x − 12 = −52?

The solution of 5x − 12 = −52 is x = -8.

How do you solve 5x − 12 = −52?

Add 12 to both sides to get 5x = -40, then divide both sides by 5 to get x = -8.

How do I check the answer?

Replace x by -8: 5(-8) − 12 = -52, which is -52.

Solve 5x − 12 = −52

How to work it out

Trying values of x in 5x − 12 = −52

Questions

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