Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

1. \(9x-2=14+x\)
2. \(-13x+13=7+7x\)
3. \(15x+7=13-11x\)
4. \(x-1=7-12x\)
5. \(-10x-10=-3+x\)
6. \(-3x+3=9+x\)
7. \(-11x-11=8+x\)
8. \(8x-3=1+5x\)
9. \(-3x+14=12+x\)
10. \(9x+15=14-13x\)
11. \(13x-6=-8+2x\)
12. \(x-3=1-10x\)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-2}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{-2}\color{blue}{+2-x } & = & 14 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & 14 \color{blue}{+2} \\\Leftrightarrow &8x & = &16\\\Leftrightarrow & \color{red}{8}x & = &16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{16}{8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+13}& = & 7 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13-7x } & = & 7 \color{red}{ +7x }\color{blue}{-13-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 7 \color{blue}{-13} \\\Leftrightarrow &-20x & = &-6\\\Leftrightarrow & \color{red}{-20}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{-6}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{3}{10} } & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+7}& = & 13 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+11x } & = & 13 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 13 \color{blue}{-7} \\\Leftrightarrow &26x & = &6\\\Leftrightarrow & \color{red}{26}x & = &6\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{6}{26} \\\Leftrightarrow & \color{green}{ x = \frac{3}{13} } & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-1}& = & 7 \color{red}{ -12x } \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1+12x } & = & 7 \color{red}{ -12x }\color{blue}{+1+12x } \\\Leftrightarrow & x \color{blue}{+12x } & = & 7 \color{blue}{+1} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+3}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-x } & = & 9 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-4x & = &6\\\Leftrightarrow & \color{red}{-4}x & = &6\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{6}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11-x } & = & 8 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 8 \color{blue}{+11} \\\Leftrightarrow &-12x & = &19\\\Leftrightarrow & \color{red}{-12}x & = &19\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{19}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{12} } & & \\ & V = \left\{ \frac{-19}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{-3}& = & 1 \color{red}{ +5x } \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3-5x } & = & 1 \color{red}{ +5x }\color{blue}{+3-5x } \\\Leftrightarrow & 8x \color{blue}{-5x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &3x & = &4\\\Leftrightarrow & \color{red}{3}x & = &4\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{4}{3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+14}& = & 12 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-x } & = & 12 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 12 \color{blue}{-14} \\\Leftrightarrow &-4x & = &-2\\\Leftrightarrow & \color{red}{-4}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-2}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+15}& = & 14 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15+13x } & = & 14 \color{red}{ -13x }\color{blue}{-15+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & 14 \color{blue}{-15} \\\Leftrightarrow &22x & = &-1\\\Leftrightarrow & \color{red}{22}x & = &-1\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-1}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{22} } & & \\ & V = \left\{ \frac{-1}{22} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-6}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-2x } & = & -8 \color{red}{ +2x }\color{blue}{+6-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & -8 \color{blue}{+6} \\\Leftrightarrow &11x & = &-2\\\Leftrightarrow & \color{red}{11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-3}& = & 1 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3+10x } & = & 1 \color{red}{ -10x }\color{blue}{+3+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & 1 \color{blue}{+3} \\\Leftrightarrow &11x & = &4\\\Leftrightarrow & \color{red}{11}x & = &4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)