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Lesson · Grade 9 · Mathematics

Solving Equations with Brackets and Like Terms

  • Grade 9
  • Mathematics
  • 2 min 19 s
  • British Columbia
  • BC9-MA-19

The video solves 3(x − 2) + x = 18 in three steps: expand the brackets to get 3x − 6 + x = 18 (warning against writing 3x − 2), collect like terms to get 4x − 6 = 18, then undo with inverse operations to get 4x = 24 and x = 6. It checks the answer by putting 6 back in, 3(4) + 6 = 18, and ends on the recap: expand, collect, undo, then check.

Concept: Equations with brackets and like terms

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In one sentence

The question this lesson answers

Let's solve 3 times the bracket x minus 2, plus x, equals 18.

An equation says the left side equals the right side. We want the x that makes this true.

Transcript

What the lesson says

Let's solve 3 times the bracket x minus 2, plus x, equals 18.

An equation says the left side equals the right side. We want the x that makes this true.

Step 1 is to expand the brackets: the 3 outside multiplies everything inside.

A term is a number, a letter, or numbers and letters multiplied together. The terms inside are x and minus 2.

3 times x is 3x, and 3 times minus 2 is minus 6. So the equation becomes 3x minus 6 plus x equals 18.

A common mistake is to multiply only the x and get 3x minus 2. The 2 is multiplied too.

Step 2 is to collect like terms: terms with the same letter part, here 3x and x.

x on its own means 1x, so 3x plus x is 4x. Now the equation is 4x minus 6 equals 18.

Step 3: undo each operation with its inverse, which reverses it. Adding undoes subtracting, and dividing undoes multiplying.

To undo minus 6, add 6 to both sides. Minus 6 plus 6 is 0, and 18 plus 6 is 24. That leaves 4x equals 24.

4x means 4 times x, so divide both sides by 4. 4x divided by 4 is x, and 24 divided by 4 is 6. So x equals 6.

Now check: put 6 in place of each x in the original equation.

Work out the brackets first: 6 minus 2 is 4. Then 3 times 4 is 12.

12 plus 6 is 18, the same as the right side, so x equals 6 is correct.

To recap: expand the brackets, collect like terms, undo each operation, then check the answer.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: multi-step one-variable linear equationsBC9-MA-19

Previous: Interpolating and extrapolating from a linear graphNext: Equations with the variable on both sides

The outcomes and strands follow the British Columbia curriculum.

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