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Lesson · Grade 9 · Mathematics

Equations with Fractions: Solve and Check

  • Grade 9
  • Mathematics
  • 2 min 11 s
  • British Columbia
  • BC9-MA-21

The video solves 1 + 2x = 3 − 2/3(x + 6) step by step: it expands the bracket, multiplies every term by the denominator 3 to clear the fraction, and gets x on its own to find x = −3/4, pointing out the common mistake of multiplying only some terms. It then puts −3/4 back into the original equation, shows that both sides come to −1/2, and ends on a one-line recap: expand, multiply every term by 3, solve, check.

Concept: Equations with fractions: solving and checking

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In one sentence

The question this lesson answers

Solve 1 plus 2x equals 3 minus two thirds times the bracket x plus 6.

Solving means finding the value of x that makes both sides equal.

Transcript

What the lesson says

Solve 1 plus 2x equals 3 minus two thirds times the bracket x plus 6.

Solving means finding the value of x that makes both sides equal.

Step 1: expand the bracket. Multiply two thirds by each term inside it, x and 6.

Two thirds of x is two thirds x, and two thirds of 6 is 4. Both are taken away from 3.

Combine the constants, the plain numbers: 3 minus 4 is negative 1.

Step 2: the fraction's denominator, its bottom number, is 3. So multiply every term on both sides by 3.

1 becomes 3, 2x becomes 6x, negative 1 becomes negative 3, and negative two thirds x becomes negative 2x.

A common mistake is multiplying only some terms, like forgetting the 1. Then the equation is no longer balanced.

Step 3: add 2x to both sides, so 3 plus 8x equals negative 3.

Subtract 3 from both sides: 8x equals negative 6.

Divide both sides by 8: x is negative 6 eighths, or negative three quarters.

Step 4: check. Substitute, or put, negative three quarters in place of each x in the original equation.

Left side: 1 plus 2 times negative three quarters is 1 minus 3 halves, or negative one half.

Right side: negative three quarters plus 6 is 21 quarters.

Two thirds of 21 quarters is 7 halves, and 3 minus 7 halves is negative one half.

Both sides equal negative one half, so the answer is correct.

To recap: expand, multiply every term by 3, solve, then check.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: multi-step one-variable linear equationsBC9-MA-21

Previous: Equations with the variable on both sides

The outcomes and strands follow the British Columbia curriculum.

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