Question

an equation is shown. (\frac{3}{2}h = 42) determine if each possible value for (h) will make this equation true or false.
true false
14
26
28
63

Explanation:

First, we solve the equation \(\frac{3}{2}h = 42\) for \(h\). Multiply both sides by \(\frac{2}{3}\) to isolate \(h\).

Step 1: Solve for \(h\)

\(h = 42\times\frac{2}{3}\)
\(h = 28\)

Now we check each value:

Step 2: Check \(h = 14\)

Substitute \(h = 14\) into \(\frac{3}{2}h\): \(\frac{3}{2}\times14 = 21
eq42\) → False

Step 3: Check \(h = 26\)

Substitute \(h = 26\) into \(\frac{3}{2}h\): \(\frac{3}{2}\times26 = 39
eq42\) → False

Step 4: Check \(h = 28\)

Substitute \(h = 28\) into \(\frac{3}{2}h\): \(\frac{3}{2}\times28 = 42\) → True

Step 5: Check \(h = 63\)

Substitute \(h = 63\) into \(\frac{3}{2}h\): \(\frac{3}{2}\times63 = 94.5
eq42\) → False

Answer:

• For \(h = 14\): False
• For \(h = 26\): False
• For \(h = 28\): True
• For \(h = 63\): False