1) His two mistakes are:
He subtract 5 from 29 and put the answer -24 instead of 24
He didn't reverse the sign of inequality when he divided it by negative number
2) Hillary bought 2.5 pounds of Granny Smith apples
3)
a) The equation has no solution
b) The equation has one solution
c) The equation has infinitely many solutions
Step-by-step explanation:
1)
In inequality, when you multiply or divide both sides by negative number, you must reverse the sign of inequality
Ex: 2 < 3, divide both sides by -1, then -2 > -3
∵ -4x + 5 > 29
- Subtract 5 from both sides
∴ -4x + 5 - 5 > 29 - 5
∴ -4x > 24
The first mistake Sam did, he write -24 instead of 24
- Divide both sides by -4
∴ -4x/-4 < 24/-4
∴ x < -6
The second mistake he didn't reverse the sign of inequality when he divided it by negative number
His two mistakes are:
He subtract 5 from 29 and put the answer -24 instead of 24
He didn't reverse the sign of inequality when he divided it by negative number
2)
Assume that Hillary buys x pound of Granny Smith apples
∵ Hillary buys 3 pounds of Gala apples
∵ Hillary buys x pound of Granny Smith apples
- Add the two numbers to find the total pounds of apples he buys
∴ He buys 3 + x pound of apples
∵ The cost of both kinds of apples is $4.50 per pound
- Multiply the number of pounds by the cost per pound
∴ The total cost = 4.5(3 + x)
∵ The total cost is $24.75
- Equate the two right sides of the total cost to find x
∴ 4.5(3 + x) = 24.75
- Multiply the bracket by 4.5
∴ 4.5(3) + 4.5(x) = 24.75
∴ 13.5 + 4.5x = 24.75
- Subtract 13.5 from both sides
∴ 4.5x = 11.25
- Divide both sides by 4.5
∴ x = 2.5
Hillary bought 2.5 pounds of Granny Smith apples
3)
a)
∵ 6x + 8 = 6(x + 2)
- Simplify the right hand side
∴ 6x + 8 = 6(x) + 6(2)
∴ 6x + 8 = 6x + 12
- Subtract 6x from both sides
∴ 8 = 12 ⇒ can not be
∵ L.H.S ≠ R.H.S
If the variable disappear from the equation and the left hand side not equal the right hand side, then the equation has no solution
∴ The equation has no solution
b)
∵ 10x = 15 + 5x
- Subtract 5x from both sides
∴ 10x - 5x = 15
∴ 5x = 15
- Divide both sides by 5
∴ x = 3
When the equation is solved and give a value of the variable, then the equation has one solution
∴ The equation has one solution
c)
∵ x + 11 = 8x + 11 - 7x
- Add the like terms in the right hand side
∴ x + 11 = (8x - 7x) + 11
∴ x + 11 = x + 11
- Subtract x from both sides
∴ 11 = 11
∵ L.H.S = R.H.s
If the variable disappear from the equation and the left hand side is equal to the right hand side, then the equation has infinitely many solutions
∴ The equation has infinitely many solutions
Learn more:
You can learn more about the equations in brainly.com/question/11306893
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