Question

When 4(9y − 5) = 10(3y + 17) − 40 is solved, the result is:

A=20.
B=25.
C=-10.
D=10.

Answer 1

`\huge\textsf{Hey there!}`

`\large\textsf{4(9y - 5) = 10(3y + 17) - 40}\\\\\large\textsf{4(9y) + 4(-5) = 10(3y) + 10(17) - 10(40)}\\\\\large\textsf{36y - 20 = 30y + 170 - 40}\\\\\large\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{36y - 20 = (30 y)+ (170 - 40)}\\\\\large\textsf{36y - 20 = 30y + 130}\\\\\large\textsf{SUBTRACT 30y to BOTH SIDES}\\\\\large\textsf{36y - 20 - 30y = 30y + 130 - 30}}\\\\\large\textsf{Cancel out: 30y - 30y because that gives you 0}\\\\\large\textsf{Keep: 20 - 30y because helps solve for the y-value}`

`\large\textsf{NEW EQUATION: 6y - 20 = 130}\\\\\large\textsf{ADD 20 to BOTH SIDES}\\\\\large\textsf{6y - 20 + 20 = 130 + 20}\\\\\large\textsf{Cancel out: -20 + 20 because that gives you 0}\\\\\large\textsf{Keep: 130 + 20 because that helps solve for the y-value}\\\\\large\textsf{130 + 20 = \bf 150}\\\\\large\textsf{NEW EQUATION: 6y = 150}\\\\\large\textsf{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{(6y)/(6)= (150)/(6)}\\\\\large\textsf{Cancel: }\mathsf{(6)/(6)\large\textsf{ because that gives you 1}}`

`\large\textsf{Keep: }\mathsf{(150)/(6)}\large\textsf{ because it helps solve for the y-value}\\\\\large\textsf{\bf y = }\mathsf{(150)/(6)}\\\\\large\textsf{OR }\\\\\mathsf{(150)/(6) }\large\textsf{ = \bf y}\\\\\\\large\textsf{SIMPLIFY ABOVE AND TOU YOU HAVE YOUR Y-VALUE}\uparrow\\\\\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf y = 25} (Option B.)}}}\huge\checkmark\\\\\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}`

Answer 2

B = 25

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Distributive Property

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality

Algebra I

• Terms/Coefficients

Explanation:

Step 1: Define

Identify

4(9y - 5) = 10(3y + 17) - 40

Step 2: Solve for y

1. [Distributive Property] Distribute 4: 36y - 20 = 10(3y + 17) - 40
2. [Distributive Property] Distribute 10: 36y - 20 = 30y + 170 - 40
3. Combine like terms: 36y - 20 = 30y + 130
4. [Subtraction Property of Equality] Subtract 30y on both sides: 6y - 20 = 130
5. [Addition Property of Equality] Add 20 on both sides: 6y = 150
6. [Division Property of Equality] Divide 6 on both sides: y = 25