Addition and Subtraction of Linear Terms

7x + 4x

-2x-9x

3x + 10 - 6x + 5

5x + 8y + 7x - y

-9x - 2y + (-x) - (-2y)

Hannah has $50. She buys 2 cups of bubble tea at $x each. She also buys 5 pancakes at $y each. How much does Hannah spend altogether?

Hannah has $50. She buys 2 cups of bubble tea at $x each. She also buys 5 pancakes at $y each. How much money does she have left?

A tube of toothpaste costs $x. A roll of dental floss costs twice as much as a tube of toothpaste. An electric toothbrush costs four times as much as a roll of dental floss. Is it correct to conclude that the electric toothbrush costs six times as much as a tube of toothpaste?

• Yes

• No

Answer explanation

Toothpaste = x.

• Dental floss = 2x (twice toothpaste).

• Electric toothbrush = 4 x (floss) = 4 X 2x = 8x.

So the toothbrush costs 8x, i.e., 8 times the toothpaste price—not 6 times.

Why not 6? You don’t add the “times” (2 + 4); you multiply them: 2×4=8.

A salesman receives a fixed monthly salary of $x. For every van he sells, he collects a commission of $y. In a particular month, he sells 6 vans. How much does he receive in total in that month?

A salesman receives a fixed monthly salary of $x. For every van he sells, he collects a commission of $y. The next month, he sells 5 vans. As a result, he receives $240 less in that month. How much commission would he have received if he sold 7 vans instead?

Answer explanation

Step 1: Write down the information

• Salary = $x

• Commission per van = $y

• Month 1 (sold 6 vans): total = $x + $6y

• Month 2 (sold 5 vans): total = $x + $5y

• Difference between Month 1 and Month 2 = $240

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Step 2: Set up the equation

(x+6y) − (x+5y) = 240

Simplify:

6y - 5y = 240

So the commission per van is $240.

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Step 3: If he sold 7 vans

Commission = 7 x $240 = $1680.

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✅ Final Answer:
If he sold 7 vans, he would receive $1680 in commission.