Question 571·Easy·Algebra

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$5x - 7 = 3$

What is the value of $x$ that satisfies the equation?

A linear equation has the variable to the first power, so you can solve it by undoing the operations around the variable. If a number is subtracted from a multiple of $x$ , add it back before finding $x$ . A Desmos regression can find the value, but don't mistake the value of $5x$ for the value of $x$ .

Hints

Hint 1
The coefficient is the number multiplying $x$ . Here, the subtraction changes the value of the whole $5x$ term. What must $5x$ equal so that subtracting $7$ gives $3$ ?
Hint 2
An inverse operation reverses another operation. Add $7$ to both sides to undo the subtraction while keeping them equal. Then you'll know the value of $5x$ , which is not yet the value of $x$ .
Hint 3
For a one-unknown equation, a Desmos regression can find the unknown. Replace $x$ with $x_{1}$ and $=$ with $\sim$ in the original equation. Read the value under PARAMETERS.

Step-by-step

Undo the subtraction, then solve in Desmos
Step 1
Find what $5x$ must equal
The $-7$ lowers $5x$ by $7$ . Undo subtraction before finding $x$ . Add $7$ to both sides to keep them equal:
$5x-7+7=3+7$ $5x=10$
So $10$ is the value of $5x$ , not yet the value of $x$ .
Step 2
Find $x$
Type the original equation as $5x_{1}-7\sim3$ in Desmos. The $x_{1}$ tells Desmos which value to find, and $\sim$ asks it to make the sides equal. Under PARAMETERS, Desmos shows $x_{1}=2$ . Since $x_{1}$ stands for $x$ , $x=2$ satisfies the equation. Choice B.

Question 571·Easy·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this