What does "solve for x" mean?

Rearrange the equation so that x is alone on one side and the other side does not contain x.

Grade 8

Algebraic expressions: practice problems

Working with algebraic expressions is the foundation for everything that follows. Make like terms, the distributive law and monomial arithmetic automatic.

Basic, Standard, Advanced: Grade 8 · Term 1

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Like terms; adding and subtracting polynomials

Terms with exactly the same letters are like terms; add their coefficients to combine them. $3x$ and $3x^2$ are not like terms.

5x - 3y - 2x + 7y = (5 - 2)x + (-3 + 7)y = 3x + 4y

When subtracting a polynomial, change the sign of every term in the brackets.

(6a - 2b) - (5a - 6b) = 6a - 2b - 5a + 6b = a + 4b

Multiplying and dividing monomials

Multiply coefficients together and letters together. To divide, write a fraction and cancel. Decide the sign first.

(-2a)^2 \times 3b = 12a^2b,\qquad 12x^2y \div 4x = \frac{12x^2y}{4x} = 3xy

For mixed $\times$ and $\div$ , put the divisor in the denominator of one fraction and cancel.

Evaluating and rearranging

To evaluate, simplify first, then substitute, putting negative values in brackets.

"Solve for $y$ " means rewrite the equation as $y = \cdots$ :

3x + 2y = 12 \;\Rightarrow\; 2y = -3x + 12 \;\Rightarrow\; y = -\frac{3}{2}x + 6

Algebraic proof

To show the sum of three consecutive integers is a multiple of 3, write them as $n,\ n+1,\ n+2$ ; the sum is $3(n + 1)$ , and $n + 1$ is an integer.

Q1BasicGr 8 · Term 1Algebraic expressions

Simplify.

(2a^{2} - 7a + 8) - (a^{2} + 7a - 6)

Answer

a^{2} - 14a + 14

Solution

Remove the brackets.
$2a^{2} - 7a + 8 - a^{2} - 7a + 6$
Combine like terms.
$= a^{2} - 14a + 14$

Q2StandardGr 8 · Term 1Algebraic expressions

Find the value of the expression when $a = 2$ and $b = -2$ .

-4a^{3}b \div (-4ab)

Answer

4

Solution

Simplify.
$-4a^{3}b \div (-4ab) = a^{2}$
Substitute the values.
$2^{2} = 4$

Q3AdvancedGr 8 · Term 1Algebraic expressions

Explain, using letters, why the sum of an even number and an odd number is odd.

Answer

For integers $m$ and $n$ , write the even number as $2m$ and the odd number as $2n + 1$ . Their sum is $2m + (2n + 1) = 2(m + n) + 1$ . Since $m + n$ is an integer, this is odd. Therefore the sum is odd.

Solution

Plan: Write the numbers as $2m$ and $2n + 1$ and rewrite the sum as $2 \times (\text{integer}) + 1$ .

Q1BasicGr 8 · Term 1Algebraic expressions

Simplify.

4(a + b)

Q2StandardGr 8 · Term 1Algebraic expressions

Find the value of the expression when $x = 4$ and $y = 4$ .

4(5x + 5y) + 2(-2x - 2y)

Q3AdvancedGr 8 · Term 1Algebraic expressions

Explain, using letters, why the sum of an even number and an odd number is odd.

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