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Solve the proportion using cross multiplication.
[tex]\[
\frac{3x + 5}{4} = \frac{x}{2}
\][/tex]

[tex]\[ x = [?] \][/tex]

Sagot :

GinnyAnswer
To solve the proportion [tex]\(\frac{3x + 5}{4} = \frac{x}{2}\)[/tex] using cross multiplication, follow these steps:

1. Set Up the Proportion:

The given proportion is:
[tex]\[ \frac{3x + 5}{4} = \frac{x}{2} \][/tex]

2. Cross Multiply:

Cross multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction:
[tex]\[ (3x + 5) \cdot 2 = x \cdot 4 \][/tex]

3. Distribute and Simplify:

Distribute the multiplication on both sides:
[tex]\[ 2(3x + 5) = 4x \][/tex]
[tex]\[ 6x + 10 = 4x \][/tex]

4. Isolate the Variable:

To isolate [tex]\(x\)[/tex], move the [tex]\(x\)[/tex] terms to one side of the equation. Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[ 6x + 10 - 4x = 4x - 4x \][/tex]
[tex]\[ 2x + 10 = 0 \][/tex]

5. Solve for [tex]\(x\)[/tex]:

Subtract 10 from both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ 2x + 10 - 10 = 0 - 10 \][/tex]
[tex]\[ 2x = -10 \][/tex]
Divide each side by 2:
[tex]\[ x = \frac{-10}{2} \][/tex]
[tex]\[ x = -5 \][/tex]

So, the solution to the equation [tex]\(\frac{3x + 5}{4} = \frac{x}{2}\)[/tex] is:
[tex]\[ x = -5 \][/tex]
Heather

Answer: x = -5

Step-by-step explanation:

      We will solve the given proportion with cross-multiplication.

Given:

  [tex]\displaystyle \frac{3x+5}{4} =\frac{x}{2}[/tex]

Cross-multiply:

  [tex]\displaystyle (3x+5)*2=x*4[/tex]

  [tex]\displaystyle 2(3x+5)=4x[/tex]

Distribute the 2 using multiplication:

  [tex]\displaystyle 6x+10=4x[/tex]

Subtract 4x and 10 from both sides of the equation:

  [tex]\displaystyle 6x-4x=-10[/tex]

Subtraction:

  [tex]\displaystyle 2x=-10[/tex]

Divide both sides of the equation by 2:

  [tex]\displaystyle x=-5[/tex]

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