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:
[tex]-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}<\dfrac{24}{-4}\ [\text{Here Sam made the second mistake}][/tex]
Dividing by negative number changes the sign of the inequality.
Thus,
[tex]x<-6[/tex]
2) Hillary buys 3 pounds of Gala apples which cost $4.50 per pound and paid
[tex]\$4.50\cdot 3=\$13.50[/tex]
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
[tex]\$4.50x+\$13.50=\$24.75[/tex]
Solve this equation
[tex]\$4.50x=\$24.75-\$13.50\\ \\4.50x=11.25\\ \\x=2.5\ kg[/tex]
of Granny Smith apples.
3) Consider all equations:
a) [tex]6x+8=6(x+2)[/tex]
Use distributive property:
[tex]6x+8=6x+12\\ \\6x+8-6x=6x+12-6x\\ \\8=12[/tex]
You get false equality, so this equation has no solutions.
b) [tex]10x=15+5x[/tex]
Add -5x:
[tex]10x-5x=15+5x-5x\\ \\5x=15\\ \\x=3\ [\text{Divide by 5}][/tex]
This equation has one solution
c) [tex]x+11=8x+11-7x[/tex]
This equation is equivalent to
[tex]x+11=(8x-7x)+11\\ \\x+11=x+11\\ \\x+11-11=x+11-11\\ \\x=x\\ \\x-x=x-x\\ \\0=0[/tex]
You get the equality that is true for all values of x, so the equation has infinitely many solutions.
