Question 104·Medium·Linear Equations in One Variable
Given the equation
what is the value of ?
For linear equations on the SAT, first distribute to clear any parentheses, then combine like terms on each side. Next, move all variable terms to one side and constants to the other using addition or subtraction on both sides. Finally, isolate the variable by dividing or adding/subtracting as needed. Work carefully with signs and arithmetic to avoid small mistakes that lead to wrong answer choices designed to match common errors.
Hints
Clear the parentheses first
Look at the right-hand side . How can you use the distributive property to remove the parentheses?
Combine like terms
After distributing, you will have several terms and constant terms. Group all terms together and all constant numbers together on each side.
Move x-terms to one side
Once the equation is simplified, get all the terms on one side of the equation (for example, by subtracting an term from both sides).
Isolate x
When you have an equation that looks like or something similar, what operation do you do on both sides to get alone?
Desmos Guide
Enter the two sides of the equation as functions
In Desmos, type y = 8x - 5 on one line and y = 3(2x + 1) + x on another line to graph both sides of the equation as separate lines.
Find the intersection point
Look for the point where the two lines intersect and tap/click it; the x-coordinate of this intersection is the value of that satisfies the equation.
Alternative: Use a single expression
You can also type 8x - 5 - (3(2x + 1) + x) and use the table feature; the value of that makes this expression equal to 0 is the solution to the equation.
Step-by-step Explanation
Distribute on the right-hand side
Start with the equation:
Distribute the across the parentheses on the right:
So the equation becomes:
Combine like terms on the right-hand side
Now combine the terms on the right side:
So the equation simplifies to:
Get all x-terms on one side
Subtract from both sides so that all terms are on the left:
which simplifies to:
Solve for x
Now isolate by adding to both sides:
which gives:
So the value of is .