Equivalent Algebraic Expressions: math practice, Grade 7 – download the PDF

1 Parts of an expression ★★★

Look at \(7x - 4y + 9\).

1. List its terms.
2. Give the coefficient of each variable term.
3. Which term is the constant?

2 Combine like terms: one variable ★★★

Simplify.

1. \(6n + 4n\)
2. \(11p - 7p\)
3. \(3k + k\)
4. \(8t - 8t\)

3 Simplify with constants ★★★

Simplify each expression by combining like terms.

1. \(4x + 7 + 2x + 1\)
2. \(9a + 5 - 3a - 2\)
3. \(10 + 6b - 4 - b\)

4 Apply the distributive property ★★★

Expand.

1. \(3(x + 5)\)
2. \(6(y - 2)\)
3. \(2(4a + 1)\)
4. \(5(3 - m)\)

5 True or false? Test with a number ★★★

Decide whether each statement is always true. Justify by substituting a value or by simplifying.

1. \(4x + 3 = 7x\)
2. \(2(x + 1) = 2x + 2\)
3. \(5x - x = 5\)
4. \(x + x = x^2\)

6 Factor a common number ★★★

Factor out the greatest common factor.

1. \(4x + 8\)
2. \(9y - 6\)
3. \(10a + 15\)
4. \(7m + 7\)

7 Phone plan ★★★

A phone plan costs 25 dollars per month plus 3 dollars for each gigabyte \(g\) of extra data.

1. Write an expression for the monthly cost.
2. Find the cost when \(g = 5\).

8 Several variables ★★★

Simplify.

1. \(5x - 3y + 2x + 7y\)
2. \(-4a + 9 - 6a - 12\)
3. \(2.5k + 4 - 0.5k - 1.5\)

9 Fraction coefficients ★★★

Simplify.

1. \(\dfrac{1}{2}x + \dfrac{3}{2}x\)
2. \(\dfrac{2}{3}y + \dfrac{1}{3}y - 5\)
3. \(\dfrac{3}{4}a - \dfrac{1}{4}a\)

10 Distribute with negatives and decimals ★★★

Expand.

1. \(-2(x + 6)\)
2. \(-3(4y - 5)\)
3. \(0.5(6a + 10)\)
4. \(-(m - 8)\)

11 Expand, then combine ★★★

Simplify.

1. \(3(x + 4) + 2x\)
2. \(5(2y - 1) - 4y\)
3. \(2(a + 3) + 3(a - 1)\)
4. \(4(m + 2) - 2(m + 5)\)

12 Factor with several terms ★★★

Factor out the GCF and check by expanding.

1. \(12x + 18\)
2. \(8y - 20\)
3. \(15a + 25b\)
4. \(6m - 9n + 12\)

13 Add and subtract expressions ★★★

Simplify.

1. \((3x + 5) + (2x - 8)\)
2. \((7a - 2) + (-3a + 6)\)
3. \((6x + 7) - (2x + 3)\)
4. \((8m + 2) - (10m - 6)\)

14 Garden bed ★★★

A garden bed is 4 meters wide and \(x + 7\) meters long.

1. Write the area as a product, then expand it.
2. Write and simplify the perimeter.
3. Find both when \(x = 5\).

15 Which are equivalent? ★★★

Which of these are equivalent to \(2(3x - 4)\)? Explain.

1. \(6x - 8\)
2. \(6x - 4\)
3. \(2 \cdot 3x - 8\)
4. \(5x - 8\)

16 Find the mistake ★★★

Two students made errors. Explain each and correct it.

1. Sam wrote \(4(x + 3) = 4x + 3\).
2. Lena wrote \(7 - 2(x + 1) = 5(x + 1)\).

17 Theater tickets ★★★

An adult ticket costs \(a\) dollars and a child ticket costs 5 dollars less. A family buys 2 adult tickets and 3 child tickets.

1. Write and simplify an expression for the total.
2. Find the total when \(a = 12\).

18 Perimeter of a triangle ★★★

The sides of a triangle measure \(2x + 3\), \(x + 5\), and \(3x - 1\) centimeters.

1. Write the perimeter in simplest form.
2. Find the perimeter when \(x = 4\).

19 Stickers ★★★

Mia has \(5n + 12\) stickers. She gives away \(2n + 5\) stickers.

1. Write an expression for the stickers she has left.
2. Find the number left when \(n = 6\).

20 Fully factored? ★★★

Two students factored \(18x + 24\): Ava wrote \(2(9x + 12)\) and Ben wrote \(6(3x + 4)\).

1. Show that both are equivalent to \(18x + 24\).
2. Whose answer is fully factored? Why?
3. Factor \(12a - 30b + 18\) completely.

21 Prove equivalence ★★★

1. Show that \(3(2x + 1) - (x - 4)\) is equivalent to \(5x + 7\).
2. Simplify \(2(3x - 1) + 4(x + 2)\), then factor the result.

22 Two gyms ★★★

Gym A charges 20 dollars to join plus 12 dollars per month: \(20 + 12m\). Gym B advertises \(12(m + 1) + 8\) dollars for \(m\) months.

1. Show that the two prices are equivalent.
2. Interpret the form \(12(m + 1) + 8\) in words.
3. Find the cost for 6 months.

23 L-shaped patio ★★★

A patio is a rectangle 10 feet wide and \(x + 8\) feet long, with a 3 foot by \(x\) foot corner removed.

1. Write an expression for the area and simplify it.
2. Find the area when \(x = 5\).

24 Find the missing number ★★★

Find the number \(k\) that makes each statement true for every \(x\).

1. \(4(x + k) + 2x = 6x + 20\)
2. \(3(2x + k) - x = 5x + 12\)