Verify a solution of an equation
Verifying a solution of an equation means substituting the proposed answer back into the original equation and checking that both sides are equal. To verify x = 5 for 3x + 2 = 17: substitute to get 3(5) + 2 = 15 + 2 = 17. Since both sides equal 17, x = 5 is confirmed. If the sides do not match, the solution is wrong. This 6th grade algebra skill from enVision Mathematics Grade 6 builds mathematical self-checking habits and deepens understanding of what it means for a value to be a solution.
Key Concepts
Property A solution of an equation is a value of a variable that makes a true statement when substituted into the equation.
To determine whether a number is a solution to an equation. Step 1. Substitute the number in for the variable in the equation. Step 2. Simplify the expressions on both sides of the equation. Step 3. Determine whether the resulting equation is true. If it is true, the number is a solution. If it is not true, the number is not a solution.
Examples Is $y=4$ a solution to $5y 3 = 17$? Substitute $y=4$: $5(4) 3 = 20 3 = 17$. Since $17=17$, yes, it is a solution. Is $x=3$ a solution to $2x + 8 = x+4$? Substitute $x=3$: $2(3) + 8 = 14$ and $3+4=7$. Since $14 \neq 7$, it is not a solution. Is $a = \frac{1}{2}$ a solution to $8a 1 = 3$? Substitute $a=\frac{1}{2}$: $8(\frac{1}{2}) 1 = 4 1 = 3$. Since $3=3$, yes, it is a solution.
Common Questions
How do you verify a solution to an equation?
Substitute the proposed value for the variable into the original equation and compute both sides. If both sides are equal, the solution is correct. For x = 5 in 3x + 2 = 17: 3(5) + 2 = 17. Verified.
What does it mean for a value to be a solution?
A value is a solution if, when substituted for the variable, it makes the equation true (both sides equal). Not every value is a solution — only the one(s) that balance the equation.
What do you do if verification fails?
If the two sides are not equal after substitution, the proposed solution is wrong. Go back and rework the problem, checking each step for errors.
What grade verifies solutions to equations?
Verifying equation solutions is a 6th grade skill in enVision Mathematics Grade 6, reinforcing both equation solving and fraction/decimal substitution.
How is verification related to the concept of equality?
An equation asserts that two expressions are equal for a specific variable value. Verification directly tests this assertion by substituting and computing.
Why is verification important in math?
Verification builds the habit of checking work — a critical skill in all fields. It catches calculation errors before they propagate and reinforces understanding of what a solution actually means.