Question

check
find the measure of aq. round your answer to the nearest tenth, if necessary.
____ cm
example 3 write and solve equations to find measurements
find the value of x and bc if b is between a and c, ac = 4x - 12, ab = x, and bc = 2x + 3.
step 1 plot two points and label them a and c. connect the points.
step 2 plot point b between points a and c.
step 3 label segments ab, bc, and ac with their given measures.
step 4 use betweenness of points to write an equation and solve for x.
ac = ab + bc
betweenness of points
4x - 12 = x + 2x + 3
substitution
4x - 12 = ____x + 3
combine like terms.
x - 12 = ____
subtract 3x from each side. simplify.
x = ____
add 12 to each side. simplify.
now find bc.
bc = 2x + 3
given
= 2(____) + 3
x = 15
= ____

Explanation:

Step1: Combine like terms on right - hand side

Since \(x + 2x=3x\), the equation \(4x - 12=x + 2x+3\) becomes \(4x - 12 = 3x+3\).

Step2: Subtract \(3x\) from each side

\(4x-3x - 12=3x-3x + 3\), so \(x - 12=3\).

Step3: Add 12 to each side

\(x-12 + 12=3 + 12\), then \(x = 15\).

Step4: Find the value of \(BC\)

Substitute \(x = 15\) into the formula \(BC=2x + 3\). So \(BC=2\times15+3=30 + 3=33\).

Answer:

In the equation \(4x - 12=x + 2x+3\), the blanks are filled as follows:

• \(4x - 12 = 3x+3\), so the first blank is \(3\).
• \(x - 12=3\), so the second blank is \(3\).
• \(x = 15\), so the third blank is \(15\).
• For \(BC=2(\underline{15})+3\), the fourth blank is \(15\).
• \(BC = 33\), so the fifth blank is \(33\).