Solve for x if 2x − 5 = 3x − 7 A. 12 B. 2 2/5 C. −2/5 D. −2 2/5

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

13. Write 0.55 as a fraction in its lowest terms.

Convert the decimal to a fraction.
$0.55 = \frac{55}{100}$
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.
$\frac{55 \div 5}{100 \div 5} = \frac{11}{20}$
The correct option is A.
$\boxed{\text{A. } \frac{11}{20}}$
14. Express 0.68 as a fraction in its lowest term.
Convert the decimal to a fraction.
$0.68 = \frac{68}{100}$
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4.
$\frac{68 \div 4}{100 \div 4} = \frac{17}{25}$
The correct option is B.
$\boxed{\text{B. } \frac{17}{25}}$
15. Subtract 125.47 from 203.90.
Perform the subtraction.
$203.90 - 125.47$
Calculate the result.
$203.90 - 125.47 = 78.43$
The correct option is B.
$\boxed{\text{B. } 78.43}$
16. Factorize $xy + 5x + 2y + 10$ .
Group the terms and factor out common factors from each group.
$xy + 5x + 2y + 10 = (xy + 5x) + (2y + 10)$ $= x(y + 5) + 2(y + 5)$
Factor out the common binomial factor $(y+5)$ .
$= (x + 2)(y + 5)$
The correct option is C.
$\boxed{\text{C. } (x+5)(y+2)}$
17. Expand $(a-2b)(a-2b)$ .
Recognize the expression as the square of a binomial
$(a-2b)^2$ .
Use the formula $(A-B)^2 = A^2 - 2AB + B^2$ , where $A=a$ and $B=2b$ .
$(a-2b)^2 = a^2 - 2(a)(2b) + (2b)^2$
Simplify the expression.
$= a^2 - 4ab + 4b^2$
The correct option is B.
$\boxed{\text{B. } a^2 - 4ab + 4b^2}$
18. Ashim is N years old now. How old will he be in 10 years?
To find Ashim's age in 10 years, add 10 to his current age.
Current age = $N$ years.
Age in 10 years = $N + 10$ years.
The correct option is B.
$\boxed{\text{B. } (N+10) \text{ years}}$
19. Solve for $x$ if $2x+5 = 3x-7$ .
Subtract $2x$ from both sides of the equation.
$5 = 3x - 2x - 7$ $5 = x - 7$
Add 7 to both sides of the equation to isolate $x$ .
$5 + 7 = x$ $x = 12$
The correct option is A.
$\boxed{\text{A. } 12}$
20. If: $27 = 6:18$ , find $a$ .

Assuming the question implies a proportion of the form $27:18 = 6:a$ .
Write the proportion as an equation of fractions.
$\frac{27}{18} = \frac{6}{a}$
Simplify the fraction on the left side.
$\frac{27}{18} = \frac{3 \times 9}{2 \times 9} = \frac{3}{2}$
Set up the simplified equation and solve for $a$ .
$\frac{3}{2} = \frac{6}{a}$
Cross-multiply:
$3a = 2 \times 6$ $3a = 12$ $a = \frac{12}{3}$ $a = 4$
The correct option is A.
$\boxed{\text{A. } 4}$

Solve for x if 2x − 5 = 3x − 7 A. 12 B. 2 2/5 C. -2/5 D. -2 2/5

Answer

Step-by-step solution

Convert the decimal to a fraction.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.

Convert the decimal to a fraction.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4.

Perform the subtraction.

Calculate the result.

Group the terms and factor out common factors from each group.

Factor out the common binomial factor $(y+5)$ .

Recognize the expression as the square of a binomial

Use the formula $(A-B)^2 = A^2 - 2AB + B^2$ , where $A=a$ and $B=2b$ .

Simplify the expression.

To find Ashim's age in 10 years, add 10 to his current age.

Subtract $2x$ from both sides of the equation.

Add 7 to both sides of the equation to isolate $x$ .

Write the proportion as an equation of fractions.

Simplify the fraction on the left side.

Set up the simplified equation and solve for $a$ .

Try one yourself

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More Mathematics Questions

Solve for x if 2x − 5 = 3x − 7 A. 12 B. 2 2/5 C. -2/5 D. -2 2/5

Answer

Step-by-step solution

Convert the decimal to a fraction.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 5.

Convert the decimal to a fraction.

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4.

Perform the subtraction.

Calculate the result.

Group the terms and factor out common factors from each group.

Factor out the common binomial factor (y+5)(y+5)(y+5).

Recognize the expression as the square of a binomial

Use the formula (A−B)2=A2−2AB+B2(A-B)^2 = A^2 - 2AB + B^2(A−B)2=A2−2AB+B2, where A=aA=aA=a and B=2bB=2bB=2b.

Simplify the expression.

To find Ashim's age in 10 years, add 10 to his current age.

Subtract $2x$ from both sides of the equation.

Add 7 to both sides of the equation to isolate xxx.

Write the proportion as an equation of fractions.

Simplify the fraction on the left side.

Set up the simplified equation and solve for aaa.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Factor out the common binomial factor $(y+5)$ .

Use the formula $(A-B)^2 = A^2 - 2AB + B^2$ , where $A=a$ and $B=2b$ .

Add 7 to both sides of the equation to isolate $x$ .

Set up the simplified equation and solve for $a$ .