To solve the given inequality:
[tex]\[
0.9x + 0.5x \geq 5.6
\][/tex]
we can follow these steps:
1. Combine like terms:
[tex]\[
(0.9 + 0.5)x \geq 5.6
\][/tex]
Simplify the coefficients on the left-hand side:
[tex]\[
1.4x \geq 5.6
\][/tex]
2. Isolate the variable [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to divide both sides of the inequality by 1.4:
[tex]\[
x \geq \frac{5.6}{1.4}
\][/tex]
3. Perform the division:
[tex]\[
x \geq 4
\][/tex]
Therefore, the solution to the inequality [tex]\( 0.9x + 0.5x \geq 5.6 \)[/tex] is:
[tex]\[
x \geq 4
\][/tex]
Thus, the correct choice is A, and you should fill in the box with:
[tex]\[
x \geq 4
\][/tex]
