Evaluate the Expression 5x-6 When x Equals -3: Step-by-Step Solution

Algebraic Substitution with Negative Values

What will be the result of this algebraic expression:

5x6 5x-6

if we place

x=3 x=-3

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's get ready to solve this problem.
00:10 First, we replace each variable with the correct number from the data.
00:17 Remember, a positive number times a negative number gives a negative result.
00:22 Great job! Let's keep calculating.
00:25 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What will be the result of this algebraic expression:

5x6 5x-6

if we place

x=3 x=-3

2

Step-by-step solution

The first step is to substitute X in the exercise, resulting in:

5(3)6 5(-3)-6

When we have two numbers with different signs, meaning one number is negative and the other is positive or vice versa,

the result of multiplication or division will always be negative.

5×3=15 5\times-3=-15

156=21 -15-6=-21

3

Final Answer

21 -21

Key Points to Remember

Essential concepts to master this topic
  • Substitution: Replace x with -3 in parentheses: 5(-3) - 6
  • Technique: Multiply first: 5 × (-3) = -15, then subtract
  • Check: Substitute -21 back: 5(-3) - 6 = -15 - 6 = -21 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to use parentheses around negative values
    Don't write 5 × -3 - 6 = 5 - 3 - 6 = -4! This ignores the multiplication order and treats the negative sign as subtraction. Always put negative values in parentheses: 5(-3) - 6.

Practice Quiz

Test your knowledge with interactive questions

What will be the result of this algebraic expression:

\( 5x-6 \)

if we place

\( x=8 \)

FAQ

Everything you need to know about this question

Why do I need parentheses around -3?

+

Parentheses make it crystal clear that you're multiplying 5 by the entire value -3. Without them, 5 × -3 might be misread as 5 - 3, leading to wrong answers!

How do I multiply a positive number by a negative number?

+

When multiplying numbers with different signs (one positive, one negative), the result is always negative. So 5×(3)=15 5 \times (-3) = -15 .

What's the difference between -15 - 6 and -15 + 6?

+

In -15 - 6, you're subtracting 6 from -15, which moves further left on the number line to -21. In -15 + 6, you'd move right to get -9.

Why isn't the answer -9?

+

That would be if you calculated 5+(3)6 5 + (-3) - 6 instead of 5×(3)6 5 \times (-3) - 6 . Remember: multiplication comes before addition/subtraction in order of operations!

How can I check if -21 is really correct?

+

Substitute back into the original expression: 5(3)6=156=21 5(-3) - 6 = -15 - 6 = -21 . Since this matches our answer, we know -21 is correct!

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