Solve for X in (2x-2)×2/5 = 5: Step-by-Step Equation

Q: Why do I multiply by 5/2 instead of dividing by 2/5?

Multiplying by the reciprocal is easier! When you have $ \times \frac{2}{5} $, multiply both sides by $ \frac{5}{2} $. This cancels out the fraction: $ \frac{2}{5} \times \frac{5}{2} = 1 $.

Q: How do I convert 29/4 to a mixed number?

Divide the numerator by the denominator: 29 ÷ 4 = 7 remainder 1. So $ \frac{29}{4} = 7\frac{1}{4} $. The quotient becomes the whole number, remainder becomes the new numerator!

Q: Can I solve this without clearing the fraction first?

Yes, but it's much harder! You could distribute the $ \frac{2}{5} $ first, but then you'd have $ 5 = \frac{4x}{5} - \frac{4}{5} $. Clearing fractions early makes the algebra much simpler.

Q: Why does my calculator show 7.25 instead of 7¼?

That's correct! $ 7\frac{1}{4} = 7.25 $ because $ \frac{1}{4} = 0.25 $. Both forms are equivalent - use whichever format the question asks for.

Linear Equations with Fractional Multiplication

$5=(2x-2)\times\frac{2}{5}$

How much is Xworth?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Multiply by the denominator to eliminate the fraction, multiply accordingly

00:18 Open parentheses properly, multiply by each factor

00:32 Arrange the equation so that only the unknown X is on one side

00:50 Isolate X

01:01 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$5=(2x-2)\times\frac{2}{5}$

How much is Xworth?

Step-by-step solution

To solve this problem, we'll perform the following calculations:

Step 1: Multiply both sides of the equation by $\frac{5}{2}$ to eliminate the fraction:

$5 \times \frac{5}{2} = (2x - 2) \times \frac{2}{5} \times \frac{5}{2}$

This simplifies to:

$\frac{25}{2} = 2x - 2$

Step 2: Solve for $x$ by isolating it on one side of the equation.

Add 2 to both sides to shift the constant:

$\frac{25}{2} + 2 = 2x - 2 + 2$

$\frac{25}{2} + \frac{4}{2} = 2x$

$\frac{29}{2} = 2x$

Step 3: Solve for $x$ by dividing both sides by 2:

$x = \frac{29}{4}$

Therefore, the solution to the problem is that $x = 7\frac{1}{4}$ .

Final Answer

$7\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both sides by reciprocal to clear fractions
Technique: Multiply by $\frac{5}{2}$ to get $\frac{25}{2} = 2x - 2$
Check: Substitute $x = 7\frac{1}{4}$ back: $(2 \times 7.25 - 2) \times \frac{2}{5} = 5$ ✓

Common Mistakes

Avoid these frequent errors

Dividing both sides by the fraction instead of multiplying by its reciprocal
Don't divide both sides by $\frac{2}{5}$ = complicated calculations! Dividing by fractions creates confusing steps and often leads to computational errors. Always multiply by the reciprocal $\frac{5}{2}$ to eliminate the fraction cleanly.

Practice Quiz

Test your knowledge with interactive questions

Solve for x:

$$ 2(4-x)=8 $$

FAQ

Everything you need to know about this question

Why do I multiply by 5/2 instead of dividing by 2/5?

Multiplying by the reciprocal is easier! When you have $\times \frac{2}{5}$ , multiply both sides by $\frac{5}{2}$ . This cancels out the fraction: $\frac{2}{5} \times \frac{5}{2} = 1$ .

How do I convert 29/4 to a mixed number?

Divide the numerator by the denominator: 29 ÷ 4 = 7 remainder 1. So $\frac{29}{4} = 7\frac{1}{4}$ . The quotient becomes the whole number, remainder becomes the new numerator!

What if I forget to add 2 to both sides?

You'll get the wrong answer! After clearing fractions, you have $\frac{25}{2} = 2x - 2$ . Always isolate the x-term by adding 2 to both sides before dividing by 2.

Can I solve this without clearing the fraction first?

Yes, but it's much harder! You could distribute the $\frac{2}{5}$ first, but then you'd have $5 = \frac{4x}{5} - \frac{4}{5}$ . Clearing fractions early makes the algebra much simpler.

Why does my calculator show 7.25 instead of 7¼?

That's correct! $7\frac{1}{4} = 7.25$ because $\frac{1}{4} = 0.25$ . Both forms are equivalent - use whichever format the question asks for.

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