The process of solving linear equations necessitates identifying the variable's value that results in a true equation. This can be achieved through distinct techniques such as substitution, elimination, or graphing. While conducting these operations, it's crucial to adhere to the equality properties—addition, subtraction, multiplication, and division—to preserve the balance of the equation.
| Topic | Problem | Solution |
|---|---|---|
| None | $2 x=4\left(\frac{1}{4}-\frac{3}{4} x\right)-6$ | \(2x = 4\left(\frac{1}{4} - \frac{3}{4}x\right) - 6\) |
| 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 | \( x=3 x+1 \) | \( x = 3x + 1 \) |
| None | The high temperature (in degrees Fahrenheit), $x$… | Given the regression line equation \(y = 8.791x - 392.966\), 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: \(4x - 2x = 2x + 1 - 2x\) which simplifies to \(2x = 1 + 7\) |
| None | $3 r+2(r-5)=25$ | Distribute the 2: \(3r + 2(r-5) = 3r + 2r - 10\) |
| None | Solve the equation. \[ 4(4+2 x)=7(x-4) \] Select … | Distribute the 4 on the left side of the equation to get \(16 + 8x\) 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, \(x+3y=7\) and \(y=2\). |
| None | Solve the equation. \[ -3 x+1+10 x=x+4 \] | Combine like terms: \( -3x + 1 + 10x = x + 4 \) becomes \( 7x + 1 = x + 4 \) |
| None | $4 x-5=35$ | The given equation is \(4x - 5 = 35\). |
| None | 21 Solve each of the following equations. (a) $4(… | (a) Distribute and combine like terms: \(4(x+1)-5(x+6)=3x+4\) becomes \(-x-26=3x+4\) |
| None | AA Speedtest by Ookla - The Global Broadband Spe.… | \( 7x - x = 12 \) |
| 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 \(21x + 42\). |
| None | \( 3 x-4=14 \) | \( 3x - 4 = 14 \) |
| None | Solve the equation. Then determine whether the eq… | The given equation is \(6x + 4 = 3x + 4\). |
| None | What value of $x$ makes this equation true? \[ \f… | Cross-multiply the equation: \(4x = -8 \times 7\) |
| 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 | $-8(-4 y-2)=-5 y+7$ | \(-8(-4y-2)=-5y+7\) |
| None | $4 x-10=18$ | Add 10 to both sides of the equation: \(4x - 10 + 10 = 18 + 10\) which simplifies to \(4x = 28\) |
| 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) \( 21 x+6=17 x-26 \) | \(21x - 17x = -26 - 6\) |
| None | (7) \( 27-11 x=x-33 \) | \( 27 - 11x = x - 33 \) |
| 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) $121-12 x=-x-4$ | \(121 - 12x = -x - 4\) |
| None | Solve the linear oquation. \[ 7 x+6=4 x+39 \] Bel… | Subtract 4x from both sides of the equation to get \(3x + 6 = 39\). |
| 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 \(8 - 4r = -2r - 10\). |