Answer:
7. [tex]x=3[/tex]
8. l=11cm and w=7 cm
9. [tex]x-5\ge12[/tex]
10. [tex]\frac{x}{3}\le15[/tex]
Step-by-step explanation:
Question 7.
The given expression is:
[tex]12-3(2x+1)=7x-3(7+x)[/tex]
Expand the parenthesis using the distributive property:
[tex]12-6x-3=7x-21-3x[/tex]
Group similar terms:
[tex]-6x-7x+3x=-21+3-12[/tex]
Simplify
[tex]-10x=-30[/tex]
Divide both sides by -10
[tex]x=3[/tex]
Question 8:
Let the width of the rectangle be; [tex]w[/tex]
The length of the rectangle is [tex]l=w+4[/tex]
The perimeter is given as: [tex]P=2(l+w)[/tex]
Given that the perimeter P=36, then:
[tex]36=2[(w+4)+w)][/tex]
[tex]\implies 36=2(2w+4)[/tex]
Divide both sides by 2:
[tex]\implies 18=2w+4[/tex]
Subtract 4 from both sides:
[tex]\implies 18-4=2w[/tex]
[tex]\implies 14=2w[/tex]
[tex]\implies w=7[/tex]
The dimensions of the rectangle is: w=7 cm and l=7+4=11cm
Question 9
Let the number be x.
"5 fewer than the number" is written as [tex]x-5[/tex]
"5 fewer than a number is at least 12" becomes
[tex]x-5\ge12[/tex]
Question 10:
Let the number be x.
The quotient of a number and 3 is written as:
[tex]\frac{x}{3}[/tex]
The quotient of a number and 3 is no more than 15 is written as;
[tex]\frac{x}{3}\le15[/tex]
