Solve 10x − 13 = −83

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

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

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

LaTeX source of the formulas on this page

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

Trying values of x in 10x − 13 = −83

x	10x − 13	Equals -83?
-9	-103	no
-8	-93	no
-7	-83	yes
-6	-73	no
-5	-63	no

Questions

What is x in 10x − 13 = −83?

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

How do you solve 10x − 13 = −83?

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

How do I check the answer?

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

Solve 10x − 13 = −83

How to work it out

Trying values of x in 10x − 13 = −83

Questions

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