Question

Please Help Me.

Answer 1

Answer:

1) First mistake: 29 - 5 = 24, not -24

Second mistake: Division by negative number changes the sign of inequality. Sam didn't change the sign.

2) 2.5 kg

3) a) no solutions

b) one solution

c) infinitely many solutions

Step-by-step explanation:

1)Sam solved the following problem:

$-4x+5>29\\ \\-4x+5-5>29-5\ [\text{Sam used the addition property}]\\ \\-4x>24\ [\text{Here Sam made a mistake, because }29-5=24\text{ not }-24]\\ \\\dfrac{-4x}{-4}$

Dividing by negative number changes the sign of the inequality.

Thus,

$x$

2) Hillary buys 3 pounds of Gala apples which cost $4.50 per pound and paid

$\ 4.50\cdot 3=\ 13.50$

Let x be the number of pounds of Granny Smith apples Hillary bought. She paid $4.50x for x pounds of Granny Smith apples.

The total cost of Hillary buying is $24.75, so

$\ 4.50x+\ 13.50=\ 24.75$

Solve this equation

$\ 4.50x=\ 24.75-\ 13.50\\ \\4.50x=11.25\\ \\x=2.5\ kg$

of Granny Smith apples.

3) Consider all equations:

a) $6x+8=6(x+2)$

Use distributive property:

$6x+8=6x+12\\ \\6x+8-6x=6x+12-6x\\ \\8=12$

You get false equality, so this equation has no solutions.

b) $10x=15+5x$

Add -5x:

$10x-5x=15+5x-5x\\ \\5x=15\\ \\x=3\ [\text{Divide by 5}]$

This equation has one solution

c) $x+11=8x+11-7x$

This equation is equivalent to

$x+11=(8x-7x)+11\\ \\x+11=x+11\\ \\x+11-11=x+11-11\\ \\x=x\\ \\x-x=x-x\\ \\0=0$

You get the equality that is true for all values of x, so the equation has infinitely many solutions.