To solve for [tex]\( a \)[/tex] to the nearest tenth in the equation [tex]\( 4a + 7x = 10 \)[/tex], follow these steps:
1. Identify the given equation:
The equation provided is [tex]\( 4a + 7x = 10 \)[/tex].
2. Assign a value to [tex]\( x \)[/tex]:
For simplicity, let’s assume [tex]\( x = 1 \)[/tex].
3. Substitute [tex]\( x \)[/tex] into the equation:
Substitute [tex]\( x = 1 \)[/tex] into the equation:
[tex]\[
4a + 7(1) = 10
\][/tex]
4. Simplify the equation:
Simplify the terms inside the equation:
[tex]\[
4a + 7 = 10
\][/tex]
5. Isolate [tex]\( a \)[/tex]:
Subtract 7 from both sides of the equation to isolate the term with [tex]\( a \)[/tex]:
[tex]\[
4a = 10 - 7
\][/tex]
[tex]\[
4a = 3
\][/tex]
6. Solve for [tex]\( a \)[/tex]:
Divide both sides by 4 to solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{3}{4}
\][/tex]
[tex]\[
a = 0.75
\][/tex]
7. Round to the nearest tenth:
Round [tex]\( 0.75 \)[/tex] to the nearest tenth:
[tex]\[
0.75 \approx 0.8
\][/tex]
Therefore, the solution for [tex]\( a \)[/tex] to the nearest tenth is [tex]\( 0.8 \)[/tex].
