Question 73·Easy·Linear Equations in One Variable
If , what is the value of ?
(Express the answer as an integer)
For linear equations in one variable, aim to isolate the variable step by step: first move constant terms to the other side using addition or subtraction, then remove coefficients by dividing or multiplying. Once you find the variable, carefully substitute it into any expression the question asks for (like here), remembering that juxtaposition means multiplication (so means ). Working in this clear order—solve for the variable, then plug in—helps you avoid common mistakes and saves time on the SAT.
Hints
Move the constant term
Look at the equation . What can you add to both sides to eliminate the ?
Get by itself
Once you have an equation of the form , what operation will isolate ?
Use to find
After you find , plug that value into . Remember that means times , not plus .
Desmos Guide
Use Desmos to find
In Desmos, type y = 5x - 15 to graph the line. Then find the x-intercept (where the graph crosses the x-axis). The x-coordinate of this intercept is the value of that satisfies .
Use Desmos to calculate
Once you know the x-value from the intercept, type 8 * (that x-value) into Desmos (for example, if the x-intercept is 3, type 8*3). The output is the value of .
Step-by-step Explanation
Isolate the term with
Start with the equation:
Add 15 to both sides to move the constant term:
Solve for
Now divide both sides of by 5 to get alone:
Find the value of
You found that . Substitute this value into :
So, the value of is 24.