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].
