Question

1. solve: ( 2(m - 3)+7<21 )

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b + c)=ab+ac\). Here \(a = 2\), \(b=m\), \(c=-3\). So \(2(m - 3)+7=2m-6 + 7\). Then \(2m-6 + 7=2m + 1\). The inequality becomes \(2m+1\lt21\).

Step2: Isolate the term with the variable

Subtract \(1\) from both sides of the inequality. Using the subtraction property of inequalities \(a\lt b\Rightarrow a - c\lt b - c\). We get \(2m+1-1\lt21 - 1\), which simplifies to \(2m\lt20\).

Step3: Solve for \(m\)

Divide both sides of the inequality by \(2\). Using the division property of inequalities \(a\lt b\), \(c>0\Rightarrow\frac{a}{c}\lt\frac{b}{c}\). So \(\frac{2m}{2}\lt\frac{20}{2}\), which gives \(m\lt10\).

The number line that represents \(m\lt10\) is the one where the arrow goes to the left from an open - circle at \(10\).

Answer:

The second option (the number line with an open - circle at \(10\) and the arrow going to the left) is the correct representation of the solution \(m\lt10\) of the inequality \(2(m - 3)+7\lt21\).