Question

solve the inequality. graph the solution.

1. ( x div 7 geq 18 )
2. ( a - 2 > 4 )
3. ( 3 leq 7 + 8 )
4. ( 8 div k leq -3 )
5. ( -12 < y - 6 )
6. ( n - 4 < 5 )
7. ( t - 5 leq -7 )
8. ( p + \frac{1}{4} geq 2 )
9. ( \frac{2}{7} > b + \frac{5}{7} )
10. ( z - 4.7 geq -1.6 )
11. ( -9.1 < d - 6.3 )
12. ( \frac{8}{5} > s + \frac{12}{5} )
13. ( -\frac{7}{8} geq m - \frac{13}{8} )
14. ( r + 0.2 < -0.7 )
15. ( h - 6 leq -8.4 )

error analysis describe and correct the

Explanation:

Step1: Solve \( x\div7\geq18 \)

Multiply both sides by 7: \( x\geq18\times7 \)
\( x\geq126 \)

Step2: Solve \( a - 2>4 \)

Add 2 to both sides: \( a>4 + 2 \)
\( a>6 \)

Step3: Solve \( 8 + k<-3 \)

Subtract 8 from both sides: \( k<-3 - 8 \)
\( k<-11 \)

Step4: Solve \( t - 5\leq-7 \)

Add 5 to both sides: \( t\leq-7 + 5 \)
\( t\leq-2 \)

Step5: Solve \( z - 4.7\geq-1.6 \)

Add 4.7 to both sides: \( z\geq-1.6 + 4.7 \)
\( z\geq3.1 \)

Step6: Solve \( -\frac{7}{8}\geq m-\frac{13}{8} \)

Add \( \frac{13}{8} \) to both sides: \( -\frac{7}{8}+\frac{13}{8}\geq m \)
\( \frac{6}{8}\geq m \)
Simplify: \( m\leq\frac{3}{4} \)

Step7: Solve \( r + 0.2<-0.7 \)

Subtract 0.2 from both sides: \( r<-0.7 - 0.2 \)
\( r<-0.9 \)

Step8: Solve \( -9.1

Add 6.3 to both sides: \( -9.1 + 6.3\( -2.8

Step9: Solve \( p+\frac{1}{4}\geq2 \)

Subtract \( \frac{1}{4} \) from both sides: \( p\geq2-\frac{1}{4} \)
\( p\geq\frac{8}{4}-\frac{1}{4} \)
\( p\geq\frac{7}{4} \) or \( p\geq1.75 \)

Step10: Solve \( -12

Add 6 to both sides: \( -12 + 6\( -6

Step11: Solve \( n - 4<5 \)

Add 4 to both sides: \( n<5 + 4 \)
\( n<9 \)

Step12: Solve \( 3\leq7 + g \)

Subtract 7 from both sides: \( 3 - 7\leq g \)
\( -4\leq g \)

Step13: Solve \( \frac{2}{7}>b+\frac{5}{7} \)

Subtract \( \frac{5}{7} \) from both sides: \( \frac{2}{7}-\frac{5}{7}>b \)
\( -\frac{3}{7}>b \) or \( b<-\frac{3}{7} \)

Step14: Solve \( \frac{8}{5}>s+\frac{12}{5} \)

Subtract \( \frac{12}{5} \) from both sides: \( \frac{8}{5}-\frac{12}{5}>s \)
\( -\frac{4}{5}>s \) or \( s<-\frac{4}{5} \)

Step15: Solve \( h - 6\leq-8.4 \)

Add 6 to both sides: \( h\leq-8.4 + 6 \)
\( h\leq-2.4 \)

Answer:

1. \( x\geq126 \)
2. \( a>6 \)
3. \( k<-11 \)
4. \( t\leq-2 \)
5. \( z\geq3.1 \)
6. \( m\leq\frac{3}{4} \)
7. \( r<-0.9 \)
8. \( -2.8
9. \( p\geq\frac{7}{4} \) (or \( p\geq1.75 \))
10. \( -6
11. \( n<9 \)
12. \( -4\leq g \)
13. \( b<-\frac{3}{7} \)
14. \( s<-\frac{4}{5} \)
15. \( h\leq-2.4 \)