QuestionРешите уравнения: 1) $4-6(x+2)=3-5x$ ; 2) $(3x-20)(4x+28)(0,2-0,06x)=0$ ; 3) $\frac{x+2}{5}-\frac{x+6}{30}=\frac{x+4}{10}+\frac{x-5}{15}$ .

Studdy Solution

STEP 1

Assumptions1. The equations are linear and quadratic equations. . We need to find the value of x that satisfies each equation.

STEP 2

Let's start with the first equation $4-6(x+2)=-5x$ . First, we need to distribute the -6 to both terms inside the parentheses.
$4-6x-12=-5x$

STEP 3

Next, we simplify the equation by combining like terms.
$-6x-8=3-5x$

STEP 4

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Let's add $x$ to both sides and add $8$ to both sides.
$-6x+x=-8+3$

STEP 5

implify the equation.
$-x=-5$

STEP 6

Finally, we divide both sides by $-1$ to solve for $x$ .
$x=5$

STEP 7

Now, let's solve the second equation $(3x-20)(4x+28)(0.2-0.06x)=0$ . This is a product of three factors equal to zero, so we can set each factor equal to zero and solve for x.
$3x-20=0$ $4x+28=0$ $0.2-0.06x=0$

STEP 8

olving the first equation gives $3x=20$ $x=\frac{20}{3}$

STEP 9

olving the second equation gives $4x=-28$ $x=-\frac{28}{4}$ $x=-7$

STEP 10

olving the third equation gives $0.06x=0.2$ $x=\frac{0.2}{0.06}$ $x\approx3.33$

STEP 11

Finally, let's solve the third equation $\frac{x+}{5}-\frac{x+6}{30}=\frac{x+4}{10}+\frac{x-5}{15}$ . To make the calculation easier, let's multiply the entire equation by30 to get rid of the fractions.
$6(x+)-x-=3(x+4)+(x-5)$

STEP 12

Next, we distribute and simplify the equation.
$6x+12-x-2=x+12+2x-10$

STEP 13

Combine like terms.
$5x+10=5x+2$

STEP 14

Subtract $x$ from both sides.
$10=2$

STEP 15

This equation has no solution because $10\neq2$ .
So, the solutions for the equations are) $x=5$ ; 2) $x=\frac{20}{3}$ , $x=-7$ , $x\approx3.33$ ; 3) No solution.

Was this helpful?

QuestionРешите уравнения: 1) $4-6(x+2)=3-5x$ ; 2) $(3x-20)(4x+28)(0,2-0,06x)=0$ ; 3) $\frac{x+2}{5}-\frac{x+6}{30}=\frac{x+4}{10}+\frac{x-5}{15}$ .

Studdy Solution

STEP 1

Assumptions1. The equations are linear and quadratic equations. . We need to find the value of x that satisfies each equation.

STEP 2

Let's start with the first equation $4-6(x+2)=-5x$ . First, we need to distribute the -6 to both terms inside the parentheses.
$4-6x-12=-5x$

STEP 3

Next, we simplify the equation by combining like terms.
$-6x-8=3-5x$

STEP 4

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Let's add $x$ to both sides and add $8$ to both sides.
$-6x+x=-8+3$

STEP 5

implify the equation.
$-x=-5$

STEP 6

Finally, we divide both sides by $-1$ to solve for $x$ .
$x=5$

STEP 7

Now, let's solve the second equation $(3x-20)(4x+28)(0.2-0.06x)=0$ . This is a product of three factors equal to zero, so we can set each factor equal to zero and solve for x.
$3x-20=0$ $4x+28=0$ $0.2-0.06x=0$

STEP 8

olving the first equation gives $3x=20$ $x=\frac{20}{3}$

STEP 9

olving the second equation gives $4x=-28$ $x=-\frac{28}{4}$ $x=-7$

STEP 10

olving the third equation gives $0.06x=0.2$ $x=\frac{0.2}{0.06}$ $x\approx3.33$

STEP 11

Finally, let's solve the third equation $\frac{x+}{5}-\frac{x+6}{30}=\frac{x+4}{10}+\frac{x-5}{15}$ . To make the calculation easier, let's multiply the entire equation by30 to get rid of the fractions.
$6(x+)-x-=3(x+4)+(x-5)$

STEP 12

Next, we distribute and simplify the equation.
$6x+12-x-2=x+12+2x-10$

STEP 13

Combine like terms.
$5x+10=5x+2$

STEP 14

Subtract $x$ from both sides.
$10=2$

STEP 15

This equation has no solution because $10\neq2$ .
So, the solutions for the equations are) $x=5$ ; 2) $x=\frac{20}{3}$ , $x=-7$ , $x\approx3.33$ ; 3) No solution.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

Assumptions1. The equations are linear and quadratic equations. . We need to find the value of x that satisfies each equation.

STEP 2

Let's start with the first equation 4−6(x+2)=−5x4-6(x+2)=-5x4−6(x+2)=−5x. First, we need to distribute the -6 to both terms inside the parentheses.4−6x−12=−5x4-6x-12=-5x4−6x−12=−5x

STEP 3

Next, we simplify the equation by combining like terms.−6x−8=3−5x-6x-8=3-5x−6x−8=3−5x

STEP 4

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Let's add xxx to both sides and add 888 to both sides.−6x+x=−8+3-6x+x=-8+3−6x+x=−8+3

STEP 5

implify the equation.−x=−5-x=-5−x=−5

STEP 6

Finally, we divide both sides by −1-1−1 to solve for xxx.x=5x=5x=5

STEP 7

STEP 8

olving the first equation gives3x=203x=203x=20x=203x=\frac{20}{3}x=320​

STEP 9

olving the second equation gives4x=−284x=-284x=−28x=−284x=-\frac{28}{4}x=−428​x=−7x=-7x=−7

STEP 10

olving the third equation gives0.06x=0.20.06x=0.20.06x=0.2x=0.20.06x=\frac{0.2}{0.06}x=0.060.2​x≈3.33x\approx3.33x≈3.33

STEP 11

STEP 12

Next, we distribute and simplify the equation.6x+12−x−2=x+12+2x−106x+12-x-2=x+12+2x-106x+12−x−2=x+12+2x−10

STEP 13

Combine like terms.5x+10=5x+25x+10=5x+25x+10=5x+2

STEP 14

Subtract xxx from both sides.10=210=210=2

STEP 15

This equation has no solution because 10≠210\neq210=2.So, the solutions for the equations are) x=5x=5x=5; 2) x=203x=\frac{20}{3}x=320​, x=−7x=-7x=−7, x≈3.33x\approx3.33x≈3.33; 3) No solution.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Let's start with the first equation $4-6(x+2)=-5x$ . First, we need to distribute the -6 to both terms inside the parentheses.
$4-6x-12=-5x$

Next, we simplify the equation by combining like terms.
$-6x-8=3-5x$

To solve for x, we need to get all the x terms on one side of the equation and the constant terms on the other side. Let's add $x$ to both sides and add $8$ to both sides.
$-6x+x=-8+3$

implify the equation.
$-x=-5$

Finally, we divide both sides by $-1$ to solve for $x$ .
$x=5$

olving the first equation gives $3x=20$ $x=\frac{20}{3}$

olving the second equation gives $4x=-28$ $x=-\frac{28}{4}$ $x=-7$

olving the third equation gives $0.06x=0.2$ $x=\frac{0.2}{0.06}$ $x\approx3.33$

Next, we distribute and simplify the equation.
$6x+12-x-2=x+12+2x-10$

Combine like terms.
$5x+10=5x+2$

Subtract $x$ from both sides.
$10=2$

This equation has no solution because $10\neq2$ .
So, the solutions for the equations are) $x=5$ ; 2) $x=\frac{20}{3}$ , $x=-7$ , $x\approx3.33$ ; 3) No solution.