Solve 7x − 10 = −52

The solution of 7x − 10 = −52 is x = -6.

7x - 10 = -52\ \Rightarrow\ x = -6

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The lines y = 7x − 10 and y = -52 meet at x = -6. 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.
$7x - 10 = -52$
2
Add 10 to both sides:
$7x - 10 + 10 = -52 + 10 \ \Rightarrow\ 7x = -42$
3
Divide both sides by 7:
$\frac{7x}{7} = \frac{-42}{7} \ \Rightarrow\ x = -6$
4
Check: put x = -6 back into the equation.
$7\cdot(-6) - 10 = -42 - 10 = -52 \checkmark$

LaTeX source of the formulas on this page

\[ 7x - 10 = -52\ \Rightarrow\ x = -6 \]
\[ 7x - 10 = -52 \]
\[ 7x - 10 + 10 = -52 + 10 \ \Rightarrow\ 7x = -42 \]
\[ \frac{7x}{7} = \frac{-42}{7} \ \Rightarrow\ x = -6 \]
\[ 7\cdot(-6) - 10 = -42 - 10 = -52 \checkmark \]

Trying values of x in 7x − 10 = −52

x	7x − 10	Equals -52?
-8	-66	no
-7	-59	no
-6	-52	yes
-5	-45	no
-4	-38	no

Questions

What is x in 7x − 10 = −52?

The solution of 7x − 10 = −52 is x = -6.

How do you solve 7x − 10 = −52?

Add 10 to both sides to get 7x = -42, then divide both sides by 7 to get x = -6.

How do I check the answer?

Replace x by -6: 7(-6) − 10 = -52, which is -52.

Solve 7x − 10 = −52

How to work it out

Trying values of x in 7x − 10 = −52

Questions

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