If x satisfies the equation \frac{3x - 1}{2} - \frac{x + 4}{5} = \frac{x + 7}{10} + 2, whi… — GRE General Test

If $x$ satisfies the equation $\frac{3x - 1}{2} - \frac{x + 4}{5} = \frac{x + 7}{10} + 2$ , which of the following statements about $x$ must be true? Indicate all such statements.

$x > 3$ Cevap
$3x$ is an integerCevap
$x$ is a solution to the equation $3x - 10 = 0$ Cevap
D
$x$ is an integer
E
$x < 3.2$

Cevap

The statements that

x > 3

, that

3x

is an integer, and that

x

is a solution to the equation

3x - 10 = 0

are all correct.

Solving the equation yields

x = \frac{10}{3} \approx 3.33

. The statement

x > 3

is correct since

3.33 > 3

. The statement that

3x

is an integer is correct because

3 \times \frac{10}{3} = 10

. The statement that

x

is a solution to

3x - 10 = 0

is correct because

3\left(\frac{10}{3}\right) - 10 = 0

Adım Adım Çözüm

Clear denominators by multiplying the entire linear equation by the least common multiple, 10.

5(3x - 1) - 2(x + 4) = (x + 7) + 20

Eliminating fractions simplifies the expression into a standard linear form.

Distribute terms across parentheses.

15x - 5 - 2x - 8 = x + 7 + 20

Expand both sides while correctly applying sign rules.

Combine like terms on each side.

13x - 13 = x + 27

Group variable terms together and constant terms together.

Isolate the variable

x

12x = 40 \implies x = \frac{40}{12} = \frac{10}{3}

Subtract

x

and add

13

on both sides, then divide by

12

Evaluate each given statement using

x = \frac{10}{3}

The value

\frac{10}{3} \approx 3.33

is greater than

3

;

3\left(\frac{10}{3}\right) = 10

is an integer;

3\left(\frac{10}{3}\right) - 10 = 0

is true;

\frac{10}{3}

is not an integer;

\frac{10}{3}

is not less than

3.2

Determine which logical assertions hold true for

x = \frac{10}{3}

Anahtar Kavram

Solving multi-step linear equations with fractions and evaluating properties of rational solutions.

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru