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Solve this inequality: [tex]4.2x + 5.6 \ \textless \ 7.2 - 8.3x[/tex]

Step 1: Isolate the constant term on the left side of the inequality.

[tex]4.2x + 5.6 \ \textless \ 7.2 - 8.3x[/tex]

Step 2: Add [tex]8.3x[/tex] to both sides of the inequality.

[tex]4.2x + 8.3x + 5.6 \ \textless \ 7.2[/tex]

Step 3: Combine like terms.

[tex]12.5x + 5.6 \ \textless \ 7.2[/tex]

Step 4: Subtract [tex]5.6[/tex] from both sides of the inequality.

[tex]12.5x \ \textless \ 1.6[/tex]

Step 5: Divide both sides by [tex]12.5[/tex].

[tex]x \ \textless \ \frac{1.6}{12.5}[/tex]

Step 6: Simplify the fraction.

[tex]x \ \textless \ 0.128[/tex]

Therefore, the solution to the inequality is [tex]x \ \textless \ 0.128[/tex].



Answer :

GinnyAnswer
To solve the inequality [tex]\( 4.2x + 5.6 < 7.2 - 8.3x \)[/tex], we will follow these steps:

1. Combine like terms:
- Move all the [tex]\(x\)[/tex]-terms to one side of the inequality and all the constant terms to the other side. To do this:
- Add [tex]\(8.3x\)[/tex] to both sides to eliminate the [tex]\(x\)[/tex]-term on the right side.
- Our inequality becomes:
[tex]\[ 4.2x + 8.3x + 5.6 < 7.2 \][/tex]

2. Simplify the [tex]\(x\)[/tex]-terms:
- Combine the like terms on the left side:
[tex]\[ 12.5x + 5.6 < 7.2 \][/tex]

3. Isolate the [tex]\(x\)[/tex]-term:
- Subtract [tex]\(5.6\)[/tex] from both sides to get the inequality in terms of [tex]\(x\)[/tex]:
[tex]\[ 12.5x < 7.2 - 5.6 \][/tex]
- Simplify the right side:
[tex]\[ 12.5x < 1.6 \][/tex]

4. Solve for [tex]\(x\)[/tex]:
- Divide both sides of the inequality by [tex]\(12.5\)[/tex]:
[tex]\[ x < \frac{1.6}{12.5} \][/tex]
- Simplify the division:
[tex]\[ x < 0.128 \][/tex]

So, the solution to the inequality [tex]\(4.2x + 5.6 < 7.2 - 8.3x\)[/tex] is [tex]\( x < 0.128 \)[/tex].

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