Problem 1: Combine like terms
Simplify \(6x+9x\).
Problem 2: Algebra tiles
The tiles show the expression \(3x + 2 + 4x + 5\). Combine the like terms to write an equivalent expression with two terms.
Problem 3: Collect terms and constants
Simplify \(7y+4+2y-9\).
Problem 4: Expand with the distributive property
Expand \(5(x+6)\).
Problem 5: Area model for expanding
The rectangle has height 7 and a total width of \(3x + 2\). Use the two areas to expand \(7(3x + 2)\).
Problem 6: Test equivalence with a table
Complete the table. Then decide which pairs of expressions appear to be equivalent, and explain how the expanded form proves it.
Problem 7: Expand with a negative factor
Expand \(-3(2x-4)\).
Problem 8: Expand and combine
Expand each expression and simplify.
- \(6(2y – 3)\)
- \(-2(5 – 3a)\)
- \(4(x + 2) + 3(x – 1)\)
Problem 9: Factor out the greatest common factor
Factor \(12x+18\) using the greatest common factor.
Problem 10: Factor out a common factor
Factor each expression using the greatest common factor.
- \(15a + 25\)
- \(8x – 12\)
- \(18m + 54\)
- \(-6y – 9\), with a negative common factor
Problem 11: Subtract an expression
Simplify \((3x+8)-(x-5)\).
Problem 12: Subtract and simplify
Simplify each expression.
- \((7x + 3) – (2x + 9)\)
- \((2m – 5) – (m – 8)\)
- \(10 – (3a + 4) + a\)
Problem 13: Rational coefficients
Simplify \(\frac{2}{3}(9x-6)+x\).
Problem 14: Decimal and fraction coefficients
Simplify each expression.
- \(0.5(6x + 10) + 1.5x\)
- \(\frac{1}{3}(12x + 9) – x\)
- \(\frac{3}{4}(8 – 4x) + x\)
Problem 15: Sales tax at the school store
A hoodie at the school store costs \(p\) dollars, and the sales tax is \(8\%\) of the price. (a) Write the total cost as \(p+0.08p\), then rewrite it as one term. (b) Find the total for a \(\$25\) hoodie. (c) Find the price of a hoodie whose total cost is \(\$54\).
Problem 16: Discount, then tax
A pair of sneakers has a regular price of \(p\) dollars. The store takes 15% off, and then sales tax of 8% is added to the sale price. (a) Write the sale price as one term. (b) Write the final cost as one term. (c) Find the final cost when the regular price is $60. (d) Find the regular price when the final cost is $91.80.
Problem 17: Perimeter of a garden bed
A rectangular garden bed has length \((3x+2)\) feet and width \((x+5)\) feet. (a) Write and simplify an expression for the perimeter. (b) Find the perimeter when \(x=3\).
Problem 18: Perimeter of a triangular bed
A triangular flower bed has sides of \((2x + 3)\) ft, \((x + 7)\) ft, and \((3x – 1)\) ft, as shown. (a) Write and simplify an expression for the perimeter. (b) Find the perimeter when \(x = 4\) and describe the triangle. (c) Find \(x\) when the perimeter is 45 ft and give the three side lengths.
Problem 19: Three ways to write a gym bill
Three friends write the monthly cost of a gym that charges $4 per class, with \(c\) classes. Ethan writes \(12 + 4c\). Maya writes \(4(c + 3)\). Noah writes \(3(c + 4) + c\). (a) Expand Maya’s and Noah’s expressions. (b) Are all three expressions equivalent? (c) Find the cost for 9 classes and for 5 classes, using the simplest form.
Problem 20: Two ways to price a jersey
A Little League jersey costs \(p\) dollars. Maya has a \(20\%\) discount and then a \(\$5\) coupon, so she pays \(p-0.20p-5\). Ethan takes the coupon first, then the discount, so he pays \(0.80(p-5)\). (a) Rewrite Maya’s expression as one with a single \(p\) term, and expand Ethan’s. (b) Are the two expressions equivalent? (c) Find what each pays when \(p=40\).
See every chapter on the Grade 7 math page.