Solving Linear Equations Introduction,Examples with Step-by-Step Explanations

The problems about Solving Linear Equations

Topic	Problem	Solution
None	$2 x = 4 (\frac{1}{4} - \frac{3}{4} x) - 6$	$2 x = 4 (\frac{1}{4} - \frac{3}{4} x) - 6$
None	The following table shows the height at half-seco…	The question asks for the height of the rock at time $t = 0$ according to the linear model \(h(t)=-…
None	a) $\frac{3 x}{4} - \frac{2 x}{3} = \frac{1}{2}$	Rewrite the equation with a common denominator of 12: \(\frac{9x}{12} - \frac{8x}{12} = \frac{1}{2}…
None	$x = 3 x + 1$	$x = 3 x + 1$
None	The high temperature (in degrees Fahrenheit), $x$ …	Given the regression line equation $y = 8.791 x - 392.966$ , where $x$ is the high temperature in…
None	$\frac{v + q}{3} = 8$	Translate the given equation into English: $\frac{v + q}{3} = 8$
None	$2 x + 1 = 4 x - 7$	Subtract 2x from both sides: $4 x - 2 x = 2 x + 1 - 2 x$ which simplifies to $2 x = 1 + 7$
None	$3 r + 2 (r - 5) = 25$	Distribute the 2: $3 r + 2 (r - 5) = 3 r + 2 r - 10$
None	Solve the equation. $4 (4 + 2 x) = 7 (x - 4)$ Select …	Distribute the 4 on the left side of the equation to get $16 + 8 x$ and distribute the 7 on the ri…
None	Solve the equation to find $x$ . \[ \begin{aligned…	Distribute the 5 on the left side of the equation and the 8 on the right side of the equation to ge…
None	If $x + 3 y = 7$ and $y = 2$ , then $x$ equals	We are given two equations, $x + 3 y = 7$ and $y = 2$ .
None	Solve the equation. $- 3 x + 1 + 10 x = x + 4$	Combine like terms: $- 3 x + 1 + 10 x = x + 4$ becomes $7 x + 1 = x + 4$
None	$4 x - 5 = 35$	The given equation is $4 x - 5 = 35$ .
None	21 Solve each of the following equations. (a) $4(…	(a) Distribute and combine like terms: $4 (x + 1) - 5 (x + 6) = 3 x + 4$ becomes $- x - 26 = 3 x + 4$
None	AA Speedtest by Ookla - The Global Broadband Spe.…	$7 x - x = 12$
None	34. What is the solution to the following equatio…	The given equation is a simple linear equation in one variable. To solve for y, we can subtract 2y …
None	Solve and check the linear equation. \[ 27-\frac{…	Multiply every term by 20 to get rid of the fractions: $20 (27 - \frac{x}{4}) = 20 (\frac{x}{5})$ , whic…
None	Solve and check the equation. \[ 3(5-2 x)=3(3 x+1…	The given equation is a linear equation in one variable, x. To solve it, we need to simplify the eq…
None	Solve the equation. $7 (3 x + 6) = 11 - (x + 2)$	Distribute the 7 on the left side of the equation to get $21 x + 42$ .
None	$3 x - 4 = 14$	$3 x - 4 = 14$
None	Solve the equation. Then determine whether the eq…	The given equation is $6 x + 4 = 3 x + 4$ .
None	What value of $x$ makes this equation true? \[ \f…	Cross-multiply the equation: $4 x = - 8 \times 7$
None	14. Solve $4 (x + 9) = 6 x - 4$ A. 3.2 B. 6.5 C. 16 D. 20	Expand the left side: 4(x+9)=4x+36
None	$- 8 (- 4 y - 2) = - 5 y + 7$	$- 8 (- 4 y - 2) = - 5 y + 7$
None	$4 x - 10 = 18$	Add 10 to both sides of the equation: $4 x - 10 + 10 = 18 + 10$ which simplifies to $4 x = 28$
None	a. $- 4 x = 360$ b. $9 + x = - 87$	$x = \frac{360}{- 4}$
None	Eric works at the deli on weekends to earn extra …	\frac{1}{2}(10(5)+14(4))
None	$3 x + 1 = 70$	$3 x + 1 = 70$
None	(8) $21 x + 6 = 17 x - 26$	$21 x - 17 x = - 26 - 6$
None	(7) $27 - 11 x = x - 33$	$27 - 11 x = x - 33$
None	Joan has a gym gift card worth $$ 100$ . Each tim…	Joan has a gym gift card worth $$ 100$ . Each time she visits the gym, $$ 12$ is deducted from the…
None	a) $121 - 12 x = - x - 4$	$121 - 12 x = - x - 4$
None	Solve the linear oquation. $7 x + 6 = 4 x + 39$ Bel…	Subtract 4x from both sides of the equation to get $3 x + 6 = 39$ .
None	Solve the equation. Be sure to check your propose…	The given equation is $x - 12 = 17$ . To solve for $x$ , we need to isolate $x$ on one side of …
None	2) $2 (4 - 2 r) = - 2 (r + 5)$	Expand the brackets on both sides of the equation to get $8 - 4 r = - 2 r - 10$ .