Answer :
To solve the problem, we need to simplify the expression [tex]\(\frac{1}{3}(2x + 12) - \frac{14}{15}x\)[/tex]. Here's a step-by-step breakdown:
1. Distribute [tex]\(\frac{1}{3}\)[/tex] inside the parenthesis:
[tex]\[
\frac{1}{3}(2x + 12) = \frac{1}{3} \times 2x + \frac{1}{3} \times 12
\][/tex]
[tex]\[
= \frac{2}{3}x + 4
\][/tex]
2. Rewrite the original expression with the distributed terms:
[tex]\[
\frac{2}{3}x + 4 - \frac{14}{15}x
\][/tex]
3. Combine like terms ([tex]\(\frac{2}{3}x\)[/tex] and [tex]\(-\frac{14}{15}x\)[/tex]):
- First, we need to find a common denominator for the fractions [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex]. The common denominator is 15.
- Convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\][/tex]
- Now combine:
[tex]\[
\frac{10}{15}x - \frac{14}{15}x = \left(\frac{10}{15} - \frac{14}{15}\right)x = -\frac{4}{15}x
\][/tex]
4. Write the expression with combined terms:
[tex]\[
4 - \frac{4}{15}x
\][/tex]
Therefore, the expression equivalent to [tex]\(\frac{1}{3}(2x + 12) - \frac{14}{15}x\)[/tex] is [tex]\(4 - \frac{4}{15}x\)[/tex].
This matches the result: [tex]\(4.0 - 0.266666666666667x\)[/tex], which represents the simplified form with [tex]\(-0.266666666666667\)[/tex] being approximately equal to [tex]\(-\frac{4}{15}\)[/tex].
1. Distribute [tex]\(\frac{1}{3}\)[/tex] inside the parenthesis:
[tex]\[
\frac{1}{3}(2x + 12) = \frac{1}{3} \times 2x + \frac{1}{3} \times 12
\][/tex]
[tex]\[
= \frac{2}{3}x + 4
\][/tex]
2. Rewrite the original expression with the distributed terms:
[tex]\[
\frac{2}{3}x + 4 - \frac{14}{15}x
\][/tex]
3. Combine like terms ([tex]\(\frac{2}{3}x\)[/tex] and [tex]\(-\frac{14}{15}x\)[/tex]):
- First, we need to find a common denominator for the fractions [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex]. The common denominator is 15.
- Convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
\][/tex]
- Now combine:
[tex]\[
\frac{10}{15}x - \frac{14}{15}x = \left(\frac{10}{15} - \frac{14}{15}\right)x = -\frac{4}{15}x
\][/tex]
4. Write the expression with combined terms:
[tex]\[
4 - \frac{4}{15}x
\][/tex]
Therefore, the expression equivalent to [tex]\(\frac{1}{3}(2x + 12) - \frac{14}{15}x\)[/tex] is [tex]\(4 - \frac{4}{15}x\)[/tex].
This matches the result: [tex]\(4.0 - 0.266666666666667x\)[/tex], which represents the simplified form with [tex]\(-0.266666666666667\)[/tex] being approximately equal to [tex]\(-\frac{4}{15}\)[/tex].
