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In algebra, we often get very long expressions that we need to make simpler. Simpler expressions are easier to solve.

# Collecting like terms

To simplify an expression, we collect like terms.

Look at the expression: 4x + 5x -2 - 2x + 7

To simplify:

• The x terms can be collected together to give 7x.
• The numbers can be collected together to give 5.

So 4x + 5x -2 - 2x + 7 simplified is 7x + 5.

Remember that terms are separated by + and - signs, and these are always attached to the front of a term.

Question

Simplify this expression: x + 5 + 3x- 7 + 9x+ 3 - 4x

To work it out:

• Write down the expression
• x + 5 + 3x - 7 + 9x + 3 - 4x
• Collect all the terms together which are alike. Remember that each term comes with an operation (+, -) which goes before it.
• x + 3x + 9x - 4x + 5 - 7 + 3
• Simplify the x terms.
• x + 3x + 9x - 4x = 9x
• Simplify the numbers separately.
• 5 - 7 + 3 = 1

Answer: x + 5 + 3x - 7 + 9x + 3 - 4x can be simplified to 9x + 1

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