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Evaluate expressions

Put numbers in for letters · Algebra 1 · 22 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Put the numbers in
  2. Powers
  3. Times and divide
  4. Plus and minus

The steps for Evaluate x^2 - 4x if x = -1. Every solution names its steps, so you always know what comes next.

Worked examples

Evaluate 3x + 2 when x = 4 Easy

The question

Question: find the value of 3x + 2 when x = 4.

3x + 2
x = 4

1 Put the numbers in

We put 4 in place of x.

3x means 3 times x.

So we write a times sign.

= 3 × 4 + 2
3x = 3 × x

2 Times and divide

Times comes before plus.

Order: ( ) → x² √ → × ÷ → + −

3 times 4 is 12.

= 12 + 2

3 Plus and minus

12 plus 2 is 14.

= 14

So 3x + 2 is 14 when x = 4.

Let's look back.

First: put the numbers in.

Then: times and divide.

Last: plus and minus.

Answer
= 14

▶ Watch it solved

Evaluate x^2 - 4x if x = -1 Medium

The question

Question: find the value of x² − 4x when x = −1.

x2 − 4x
x = −1

1 Put the numbers in

We put −1 in place of x.

4x means 4 times x.

So we write a times sign.

A negative number goes in brackets, so its minus stays with it.

= (−1)2 − 4 × (−1)
4x = 4 × x

2 Powers

Powers come before minus and times.

Order: ( ) → x² √ → × ÷ → + −

(−1)² means −1 times −1.

Minus times minus is plus.

(−1)2 = (−1) × (−1) = 1

That is 1.

= 1 − 4 × (−1)

3 Times and divide

Times comes before minus.

+ × − = −

Plus times minus is minus.

4 times 1 is 4.

So we get −4.

= 1 − (−4)

4 Plus and minus

Taking away a negative is the same as adding.

− (−) = +

So 1 − (−4) becomes 1 + 4.

= 1 + 4

1 plus 4 is 5.

= 5

So x² − 4x is 5 when x = −1.

Let's look back.

First: put the numbers in.

Then: powers.

Then: times and divide.

Last: plus and minus.

Answer
= 5

▶ Watch it solved

Evaluate 2x^2 - 3x + 1 when x = -2 Harder

The question

Question: find the value of 2x² − 3x + 1 when x = −2.

2x2 − 3x + 1
x = −2

1 Put the numbers in

We put −2 in place of x.

2x² means 2 times x².

So we write a times sign.

A negative number goes in brackets, so its minus stays with it.

= 2 × (−2)2 − 3 × (−2) + 1
2x² = 2 × x²

2 Powers

Powers come before times, minus and plus.

Order: ( ) → x² √ → × ÷ → + −

(−2)² means −2 times −2.

Minus times minus is plus.

(−2)2 = (−2) × (−2) = 4

That is 4.

= 2 × 4 − 3 × (−2) + 1

3 Times and divide

Times comes before minus and plus.

Times and divide: we go from left to right.

same kind: left → right

2 times 4 is 8.

= 8 − 3 × (−2) + 1

Times comes before minus and plus.

+ × − = −

Plus times minus is minus.

3 times 2 is 6.

So we get −6.

= 8 − (−6) + 1

4 Plus and minus

Plus and minus: we go from left to right.

Taking away a negative is the same as adding.

same kind: left → right
− (−) = +

So 8 − (−6) becomes 8 + 6.

= 8 + 6 + 1

8 plus 6 is 14.

= 14 + 1

14 plus 1 is 15.

= 15

So 2x² − 3x + 1 is 15 when x = −2.

Let's look back.

First: put the numbers in.

Then: powers.

Then: times and divide.

Last: plus and minus.

Answer
= 15

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. 3x + 2 when x = 4
    Answer
    = 14
  2. 5a - 1 when a = 3
    Answer
    = 14
  3. 2x + 3y when x = 1, y = 4
    Answer
    = 14
  4. 10 - 2n when n = 3
    Answer
    = 4
  5. 3(x - 2) when x = 7
    Answer
    = 15
  6. x^2 + 1 when x = 3
    Answer
    = 10
  7. 7 - y when y = 7
    Answer
    = 0
  8. 6m when m = -2
    Answer
    = −12
  9. 4p + 5 when p = 0
    Answer
    = 5
  10. 2a + b when a = 6, b = 3
    Answer
    = 15

Medium

  1. x^2 - 4x if x = -1
    Answer
    = 5
  2. evaluate 3a^2 - b for a = 2 and b = 5
    Answer
    = 7
  3. -x^2 when x = 3
    Answer
    = −9
  4. 4x - 3y when x = 2, y = -3
    Answer
    = 17
  5. ab - 2b when a = 5, b = 3
    Answer
    = 9
  6. 2(x + y) when x = 4, y = -6
    Answer
    = −4
  7. 5 - 3k when k = -2
    Answer
    = 11
  8. m^2 + n^2 when m = 3, n = 4
    Answer
    = 25

Harder

  1. 2x^2 - 3x + 1 when x = -2
    Answer
    = 15
  2. -x^2 + 5x when x = -1
    Answer
    = −6
  3. (a - b)^2 when a = 3, b = 7
    Answer
    = 16
  4. 2x^3 - x when x = -1
    Answer
    = −1