Question

q is between m and n. mn = x + 22, mq = 16 + 2x, and nq = 12. draw and label the segment. x = mq =

Explanation:

Step1: Use segment - addition postulate

Since \(Q\) is between \(M\) and \(N\), we have \(MQ + NQ=MN\). Substituting the given expressions: \((16 + 2x)+12=x + 22\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(16+12 + 2x=x + 22\), which gives \(28+2x=x + 22\).

Step3: Isolate the variable \(x\)

Subtract \(x\) from both sides: \(28+2x - x=x + 22 - x\), resulting in \(28+x=22\). Then subtract 28 from both sides: \(x=22 - 28\).

Step4: Calculate the value of \(x\)

\(x=-6\).

Step5: Calculate the value of \(MQ\)

Substitute \(x = - 6\) into the expression for \(MQ\): \(MQ=16+2x=16+2\times(-6)=16 - 12 = 4\).

Answer:

\(x=-6\)
\(MQ = 4\)