Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+11}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11-x } & = & 8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 8 \color{blue}{-11} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-3}& = & -14 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3-8x } & = & -14 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-13x & = &-11\\\Leftrightarrow & \color{red}{-13}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+10}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10-9x } & = & 6 \color{red}{ +9x }\color{blue}{-10-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 6 \color{blue}{-10} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-4}& = & 1 \color{red}{ -14x } \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4+14x } & = & 1 \color{red}{ -14x }\color{blue}{+4+14x } \\\Leftrightarrow & 15x \color{blue}{+14x } & = & 1 \color{blue}{+4} \\\Leftrightarrow &29x & = &5\\\Leftrightarrow & \color{red}{29}x & = &5\\\Leftrightarrow & \frac{\color{red}{29}x}{ \color{blue}{ 29}} & = & \frac{5}{29} \\\Leftrightarrow & \color{green}{ x = \frac{5}{29} } & & \\ & V = \left\{ \frac{5}{29} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{-14}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14-x } & = & 6 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 6 \color{blue}{+14} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11-x } & = & 11 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 11 \color{blue}{-11} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{-9}& = & 4 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9+2x } & = & 4 \color{red}{ -2x }\color{blue}{+9+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 4 \color{blue}{+9} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+2}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -14 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -14 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-16\\\Leftrightarrow & \color{red}{-15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{16}{15} } & & \\ & V = \left\{ \frac{16}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+14}& = & -14 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x } & = & -14 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &13x & = &-28\\\Leftrightarrow & \color{red}{13}x & = &-28\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-28}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{13} } & & \\ & V = \left\{ \frac{-28}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-4}& = & -7 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4-5x } & = & -7 \color{red}{ +5x }\color{blue}{+4-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -7 \color{blue}{+4} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{+9}& = & -5 \color{red}{ -13x } \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9+13x } & = & -5 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & 9x \color{blue}{+13x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &22x & = &-14\\\Leftrightarrow & \color{red}{22}x & = &-14\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{-14}{22} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+8}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8-x } & = & 3 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 3 \color{blue}{-8} \\\Leftrightarrow &14x & = &-5\\\Leftrightarrow & \color{red}{14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)