Solve 7x − 13 = −83

The solution of 7x − 13 = −83 is x = -10.

7x - 13 = -83\ \Rightarrow\ x = -10

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The lines y = 7x − 13 and y = -83 meet at x = -10. 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.
$7x - 13 = -83$
2
Add 13 to both sides:
$7x - 13 + 13 = -83 + 13 \ \Rightarrow\ 7x = -70$
3
Divide both sides by 7:
$\frac{7x}{7} = \frac{-70}{7} \ \Rightarrow\ x = -10$
4
Check: put x = -10 back into the equation.
$7\cdot(-10) - 13 = -70 - 13 = -83 \checkmark$

LaTeX source of the formulas on this page

\[ 7x - 13 = -83\ \Rightarrow\ x = -10 \]
\[ 7x - 13 = -83 \]
\[ 7x - 13 + 13 = -83 + 13 \ \Rightarrow\ 7x = -70 \]
\[ \frac{7x}{7} = \frac{-70}{7} \ \Rightarrow\ x = -10 \]
\[ 7\cdot(-10) - 13 = -70 - 13 = -83 \checkmark \]

Trying values of x in 7x − 13 = −83

x	7x − 13	Equals -83?
-12	-97	no
-11	-90	no
-10	-83	yes
-9	-76	no
-8	-69	no

Questions

What is x in 7x − 13 = −83?

The solution of 7x − 13 = −83 is x = -10.

How do you solve 7x − 13 = −83?

Add 13 to both sides to get 7x = -70, then divide both sides by 7 to get x = -10.

How do I check the answer?

Replace x by -10: 7(-10) − 13 = -83, which is -83.

Solve 7x − 13 = −83

How to work it out

Trying values of x in 7x − 13 = −83

Questions

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