Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+10}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & -4x \color{red}{+10}\color{blue}{-10-3x } & = & -9 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & -4x \color{blue}{-3x } & = & -9 \color{blue}{-10} \\\Leftrightarrow &-7x & = &-19\\\Leftrightarrow & \color{red}{-7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{+10}& = & -14 \color{red}{ -9x } \\\Leftrightarrow & -x \color{red}{+10}\color{blue}{-10+9x } & = & -14 \color{red}{ -9x }\color{blue}{-10+9x } \\\Leftrightarrow & -x \color{blue}{+9x } & = & -14 \color{blue}{-10} \\\Leftrightarrow &8x & = &-24\\\Leftrightarrow & \color{red}{8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-24}{8} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+11}& = & 6 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11+9x } & = & 6 \color{red}{ -9x }\color{blue}{-11+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 6 \color{blue}{-11} \\\Leftrightarrow &23x & = &-5\\\Leftrightarrow & \color{red}{23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+11}& = & -8 \color{red}{ +2x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-2x } & = & -8 \color{red}{ +2x }\color{blue}{-11-2x } \\\Leftrightarrow & -13x \color{blue}{-2x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-15x & = &-19\\\Leftrightarrow & \color{red}{-15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-19}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{19}{15} } & & \\ & V = \left\{ \frac{19}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{+4}& = & 10 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{+4}\color{blue}{-4-5x } & = & 10 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+1}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1-14x } & = & -11 \color{red}{ +14x }\color{blue}{-1-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -11 \color{blue}{-1} \\\Leftrightarrow &-27x & = &-12\\\Leftrightarrow & \color{red}{-27}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-12}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-12}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12-7x } & = & -3 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -3 \color{blue}{+12} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+7}& = & -2 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+8x } & = & -2 \color{red}{ -8x }\color{blue}{-7+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -2 \color{blue}{-7} \\\Leftrightarrow &9x & = &-9\\\Leftrightarrow & \color{red}{9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-9}{9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+6}& = & -8 \color{red}{ -8x } \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6+8x } & = & -8 \color{red}{ -8x }\color{blue}{-6+8x } \\\Leftrightarrow & x \color{blue}{+8x } & = & -8 \color{blue}{-6} \\\Leftrightarrow &9x & = &-14\\\Leftrightarrow & \color{red}{9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+11}& = & -10 \color{red}{ +5x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-5x } & = & -10 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & -8x \color{blue}{-5x } & = & -10 \color{blue}{-11} \\\Leftrightarrow &-13x & = &-21\\\Leftrightarrow & \color{red}{-13}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{21}{13} } & & \\ & V = \left\{ \frac{21}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+10}& = & -3 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+10}\color{blue}{-10-7x } & = & -3 \color{red}{ +7x }\color{blue}{-10-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -3 \color{blue}{-10} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+8}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8-x } & = & 11 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 11 \color{blue}{-8} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)