Question 406·Easy·Algebra

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Solve for $x$ in the equation

3x - 7 = 2x + 5.

Your answer

A linear equation with $x$ on both sides can be solved by keeping the sides equal while you move the $x$ -terms together. On a timed test, Desmos can solve the original equation directly, even when the arithmetic looks short. Whatever you subtract from one side, subtract from the other side too. Watch the sign when you move a negative number.

Hints

Hint 1
The terms $3x$ and $2x$ differ by one $x$ . Subtract $2x$ from both sides so you can see what that remaining $x$ must do.
Hint 2
After the $x$ -terms are together, $x$ still has $7$ subtracted from it. What must you add to both sides to leave $x$ alone?

Step-by-step

Keep both sides equal, then confirm in Desmos
Step 1
Bring the x-terms together
The equation has $3x$ on the left and $2x$ on the right. Subtract $2x$ from both sides so only one $x$ remains: $x-7=5$ . Subtracting it from only one side would change the equation.
Step 2
Isolate x
Add $7$ to both sides of $x-7=5$ to undo subtracting $7$ : $x=5+7$ .
Step 3
Find the value of x
Type the original equation in Desmos as $3x_{1}-7\sim 2x_{1}+5$ . Use $x_{1}$ for the unknown and $\sim$ to tell Desmos to find where the sides are equal. Then type $5+7$ to evaluate the expression from the previous step. Under PARAMETERS, Desmos shows $x_{1}=12$ , and the $5+7$ line prints $12$ . So the solution is $x=12$ . Grid in 12.

Question 406·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this