Question

Simplify 7/9h +10 - 4/9h -3
A. 3/18h sqared +7=1/6h squared +7
B. 3/9h squared +7 =1/3h squared +7
C. 3/18h ×7 = 1/6h+ 7
D. 3/9h ×7 = 1/3h ×7

Answer 1

To simplify the expression \( \frac{7}{9}h + 10 - \frac{4}{9}h - 3 \), let's combine like terms step by step.

1. Start with the expression:
\[
\frac{7}{9}h - \frac{4}{9}h + 10 - 3
\]

2. Combine the terms with \( h \):
\[
\left(\frac{7}{9} - \frac{4}{9}\right)h = \frac{3}{9}h = \frac{1}{3}h
\]

3. Combine the constant terms:
\[
10 - 3 = 7
\]

4. Now, combine everything:
\[
\frac{1}{3}h + 7
\]

This means the simplified expression is:
\[
\frac{1}{3}h + 7
\]

Now, examining the options provided:
A. \( \frac{3}{18}h^2 + 7 = \frac{1}{6}h^2 + 7 \) --> This is incorrect since we have a linear expression, not quadratic.
B. \( \frac{3}{9}h^2 + 7 = \frac{1}{3}h^2 + 7 \) --> This is also incorrect for the same reason.
C. \( \frac{3}{18}h \times 7 = \frac{1}{6}h + 7 \) --> Not correct, interpreting incorrectly.
D. \( \frac{3}{9}h \times 7 = \frac{1}{3}h \times 7 \) --> This is incorrect since we are not multiplying by 7 here.

None of the options represent the simplified expression \( \frac{1}{3}h + 7 \).

Thus, the solution doesn't match any of the provided options.