Question

solve for a.
7a + 17a - 14a - 8a = 14
submit
a =

Explanation:

Step1: Combine like terms

First, combine the terms with \(a\): \(7a + 17a - 8a=(7 + 17 - 8)a = 16a\). Then combine the constant terms: \(-149\) (wait, maybe it's a typo? Let's assume the equation is \(7a + 17a - 149 - 8a = 14\) or maybe \(7a + 17a - 14 - 8a = 14\)? Wait, looking at the image, maybe the equation is \(7a + 17a - 14 - 8a = 14\)? Wait, let's re-express. Let's take the equation as \(7a + 17a - 8a - 14 = 14\) (assuming the middle term is -14). So combining \(a\) terms: \(7a + 17a - 8a = (7 + 17 - 8)a = 16a\). Then the equation becomes \(16a - 14 = 14\).

Step2: Isolate the term with \(a\)

Add 14 to both sides: \(16a - 14 + 14 = 14 + 14\), which simplifies to \(16a = 28\).

Step3: Solve for \(a\)

Divide both sides by 16: \(a=\frac{28}{16}=\frac{7}{4}=1.75\). Wait, maybe the original equation was \(7a + 17a - 149 - 8a = 14\)? Let's check again. If the equation is \(7a + 17a - 149 - 8a = 14\), then combining \(a\) terms: \(7a + 17a - 8a = 16a\), and constants: \(-149\). So equation is \(16a - 149 = 14\). Then add 149 to both sides: \(16a = 14 + 149 = 163\), so \(a=\frac{163}{16}\approx10.1875\). But the image is a bit unclear. Wait, maybe the equation is \(7a + 17a - 14 - 8a = 14\). Let's do that:

Combine \(a\) terms: \(7a + 17a - 8a = 16a\).

Combine constants: \(-14\).

Equation: \(16a - 14 = 14\).

Add 14 to both sides: \(16a = 28\).

Divide by 16: \(a = \frac{28}{16} = \frac{7}{4} = 1.75\).

Alternatively, if the middle term is -149, then:

\(7a + 17a - 8a - 149 = 14\)

\(16a - 149 = 14\)

\(16a = 163\)

\(a = \frac{163}{16} = 10.1875\)

But maybe the correct equation is \(7a + 17a - 14 - 8a = 14\), so let's proceed with that.

Answer:

\(a = \frac{7}{4}\) (or \(1.75\))