Question 109·Easy·Linear Equations in One Variable
If what is the value of ?
(Express the answer as an integer)
For one-variable linear equations of the form (fraction)·variable plus a constant equals a number, isolate the variable step by step: first undo addition or subtraction to get the term with the variable alone on one side, then undo multiplication or division (including fractional coefficients) on the variable. Remember that dividing by a fraction is the same as multiplying by its reciprocal—this keeps arithmetic quick and reduces mistakes on the SAT.
Hints
Undo the constant term first
Look at the in the equation. What operation can you do on both sides to remove this ?
Simplify after removing 7
After you remove the , what number should be on the right-hand side of the equation?
Handle the fraction coefficient
Once you have an equation of the form , how do you isolate ? Remember that dividing by a fraction is the same as multiplying by its reciprocal.
Desmos Guide
Graph the equation and a horizontal line
In Desmos, enter y = (3/2)x + 7 on one line and y = 31 on another line so you can see where the line from the equation equals 31.
Find the intersection point
Click on the point where the two graphs intersect; the x-coordinate of this intersection is the value of that solves the equation.
Step-by-step Explanation
Isolate the term with
Start with the equation:
To isolate the term with , subtract 7 from both sides:
This simplifies to:
Solve for by undoing the multiplication
Now you have:
To undo the multiplication by , divide both sides by , which is the same as multiplying by its reciprocal :
Compute this product:
So the value of is .