Students solve 12 equations with the variable on both sides, spot no-solution and infinite-solution cases, and compare two gym price plans.
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A balance picture with 5x − 4 on one pan and 2x + 11 on the other opens the page. The worked example takes 2x from both sides, adds 4, divides by 3, and checks that x = 5 makes both sides equal 21. Students then solve equations with integer answers, including negatives and zero, decide for two items whether there is one solution, none or infinitely many, and compare the costs of two climbing gyms. The key shows the collected step before each answer.
Problem 7, 10c − 6 = 13c − 6, has the answer c = 0. Students who see −6 on both sides often call it no solution; have them finish the steps to 0 = 3c and compare it with the −8 = 5 they reach in the first What Happens? item.
In problem 12, −4(a + 3) becomes −4a − 12. Students who write −4a + 12 get a = 1 instead of −3, so have them check the answer in both sides.
For Gym Plans, some students write 35v + 4 for Peak. Ask what one visit adds at each gym, then check that v = 7 gives the same total, 63, on both plans.
Ways to adjust the 12 equations and the gym problem.
Each one is checked against the official document. Where the resource covers only part of a standard, the note says so.
Students solve equations with the letter on both sides, including ones with negative numbers and brackets, check a worked answer, and write and solve an equation comparing two gym plans. Decimal numbers are not used, and the no-solution and endless-solution items go past this expectation.
To solve each equation, students collect the letter terms on one side by adding or subtracting them. This is a step inside each problem rather than practice on its own, and adding binomials is not covered.
Yes. All 12 equations solve to integers from −7 to 8, and the gym problem comes to 7 visits, so students can focus on the steps.
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