Solve 12x − 13 = −97

The solution of 12x − 13 = −97 is x = -7.

12x - 13 = -97\ \Rightarrow\ x = -7

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The lines y = 12x − 13 and y = -97 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.
$12x - 13 = -97$
2
Add 13 to both sides:
$12x - 13 + 13 = -97 + 13 \ \Rightarrow\ 12x = -84$
3
Divide both sides by 12:
$\frac{12x}{12} = \frac{-84}{12} \ \Rightarrow\ x = -7$
4
Check: put x = -7 back into the equation.
$12\cdot(-7) - 13 = -84 - 13 = -97 \checkmark$

LaTeX source of the formulas on this page

\[ 12x - 13 = -97\ \Rightarrow\ x = -7 \]
\[ 12x - 13 = -97 \]
\[ 12x - 13 + 13 = -97 + 13 \ \Rightarrow\ 12x = -84 \]
\[ \frac{12x}{12} = \frac{-84}{12} \ \Rightarrow\ x = -7 \]
\[ 12\cdot(-7) - 13 = -84 - 13 = -97 \checkmark \]

Trying values of x in 12x − 13 = −97

x	12x − 13	Equals -97?
-9	-121	no
-8	-109	no
-7	-97	yes
-6	-85	no
-5	-73	no

Questions

What is x in 12x − 13 = −97?

The solution of 12x − 13 = −97 is x = -7.

How do you solve 12x − 13 = −97?

Add 13 to both sides to get 12x = -84, then divide both sides by 12 to get x = -7.

How do I check the answer?

Replace x by -7: 12(-7) − 13 = -97, which is -97.

Solve 12x − 13 = −97

How to work it out

Trying values of x in 12x − 13 = −97

Questions

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