Question
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a. \( 2 x+4=-18 \) b. \( -5 x+5=-20 \) c. \( 3 x-26=46 \) d. \( 17 x-18=-5 \) e. \( 3 x=24 \) f. \( 5 x+10=20 \) g. \( 2 x=-8 \) h. \( -5+8 x=-29 \)

Ask by Luna Santiago. in Colombia
Nov 23,2024

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Answer

a. \( x = -11 \) b. \( x = 5 \) c. \( x = 24 \) d. \( x = \frac{13}{17} \) e. \( x = 8 \) f. \( x = 2 \) g. \( x = -4 \) h. \( x = -3 \)

Solution

Aquí están las soluciones para cada una de las ecuaciones: a. \( 2x + 4 = -18 \) Restamos 4 de ambos lados: \[ 2x = -18 - 4 \] \[ 2x = -22 \] Dividimos entre 2: \[ x = -11 \] b. \( -5x + 5 = -20 \) Restamos 5 de ambos lados: \[ -5x = -20 - 5 \] \[ -5x = -25 \] Dividimos entre -5: \[ x = 5 \] c. \( 3x - 26 = 46 \) Sumamos 26 a ambos lados: \[ 3x = 46 + 26 \] \[ 3x = 72 \] Dividimos entre 3: \[ x = 24 \] d. \( 17x - 18 = -5 \) Sumamos 18 a ambos lados: \[ 17x = -5 + 18 \] \[ 17x = 13 \] Dividimos entre 17: \[ x = \frac{13}{17} \] e. \( 3x = 24 \) Dividimos entre 3: \[ x = \frac{24}{3} \] \[ x = 8 \] f. \( 5x + 10 = 20 \) Restamos 10 de ambos lados: \[ 5x = 20 - 10 \] \[ 5x = 10 \] Dividimos entre 5: \[ x = 2 \] g. \( 2x = -8 \) Dividimos entre 2: \[ x = \frac{-8}{2} \] \[ x = -4 \] h. \( -5 + 8x = -29 \) Sumamos 5 a ambos lados: \[ 8x = -29 + 5 \] \[ 8x = -24 \] Dividimos entre 8: \[ x = \frac{-24}{8} \] \[ x = -3 \] Resumiendo las soluciones: a. \( x = -11 \) b. \( x = 5 \) c. \( x = 24 \) d. \( x = \frac{13}{17} \) e. \( x = 8 \) f. \( x = 2 \) g. \( x = -4 \) h. \( x = -3 \)

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Let's dive into solving these equations! For equation (a) \( 2x + 4 = -18 \), start by isolating \( x \). You'll first subtract 4 from both sides to get \( 2x = -22 \), then divide by 2, resulting in \( x = -11 \). Get ready for equation (b) \( -5x + 5 = -20 \). Subtract 5 from both sides to get \( -5x = -25 \), and dividing by -5 gives you \( x = 5 \). For equation (c) \( 3x - 26 = 46 \), adding 26 to both sides results in \( 3x = 72 \), and dividing by 3 gives \( x = 24 \). Moving on to equation (d) \( 17x - 18 = -5 \), add 18 to both sides to have \( 17x = 13 \) and then divide by 17 to find \( x = \frac{13}{17} \). For (e) \( 3x = 24 \), simply divide both sides by 3 to find \( x = 8 \). In (f) \( 5x + 10 = 20 \), subtract 10 from both sides leading to \( 5x = 10 \). Finally, divide by 5 for \( x = 2 \). Next, in equation (g) \( 2x = -8 \), just divide by 2 to get \( x = -4 \). And for (h) \( -5 + 8x = -29 \), add 5 to both sides giving you \( 8x = -24 \) and divide by 8 to solve for \( x = -3 \). Now you've got all the answers ready! Let’s summarize those solutions: a) -11, b) 5, c) 24, d) \(\frac{13}{17}\), e) 8, f) 2, g) -4, h) -3. 🚀 Happy solving!

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