Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+2}& = & 5 \color{red}{ -13x } \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2+13x } & = & 5 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & -10x \color{blue}{+13x } & = & 5 \color{blue}{-2} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-1}& = & -8 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1+11x } & = & -8 \color{red}{ -11x }\color{blue}{+1+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -8 \color{blue}{+1} \\\Leftrightarrow &15x & = &-7\\\Leftrightarrow & \color{red}{15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{15} } & & \\ & V = \left\{ \frac{-7}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-11}& = & -3 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11+9x } & = & -3 \color{red}{ -9x }\color{blue}{+11+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -3 \color{blue}{+11} \\\Leftrightarrow &23x & = &8\\\Leftrightarrow & \color{red}{23}x & = &8\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{8}{23} \\\Leftrightarrow & \color{green}{ x = \frac{8}{23} } & & \\ & V = \left\{ \frac{8}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{+8}& = & 5 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{+8}\color{blue}{-8+5x } & = & 5 \color{red}{ -5x }\color{blue}{-8+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 5 \color{blue}{-8} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+7}& = & -6 \color{red}{ +15x } \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7-15x } & = & -6 \color{red}{ +15x }\color{blue}{-7-15x } \\\Leftrightarrow & -7x \color{blue}{-15x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &-22x & = &-13\\\Leftrightarrow & \color{red}{-22}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-22}x}{ \color{blue}{ -22}} & = & \frac{-13}{-22} \\\Leftrightarrow & \color{green}{ x = \frac{13}{22} } & & \\ & V = \left\{ \frac{13}{22} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{+7}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7+11x } & = & -13 \color{red}{ -11x }\color{blue}{-7+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &17x & = &-20\\\Leftrightarrow & \color{red}{17}x & = &-20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{17} } & & \\ & V = \left\{ \frac{-20}{17} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+5}& = & 6 \color{red}{ +9x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-9x } & = & 6 \color{red}{ +9x }\color{blue}{-5-9x } \\\Leftrightarrow & -2x \color{blue}{-9x } & = & 6 \color{blue}{-5} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-14}& = & 7 \color{red}{ +11x } \\\Leftrightarrow & 7x \color{red}{-14}\color{blue}{+14-11x } & = & 7 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 7x \color{blue}{-11x } & = & 7 \color{blue}{+14} \\\Leftrightarrow &-4x & = &21\\\Leftrightarrow & \color{red}{-4}x & = &21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{4} } & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+4}& = & 9 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & 9 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 9 \color{blue}{-4} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+6}& = & -10 \color{red}{ -5x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6+5x } & = & -10 \color{red}{ -5x }\color{blue}{-6+5x } \\\Leftrightarrow & 13x \color{blue}{+5x } & = & -10 \color{blue}{-6} \\\Leftrightarrow &18x & = &-16\\\Leftrightarrow & \color{red}{18}x & = &-16\\\Leftrightarrow & \frac{\color{red}{18}x}{ \color{blue}{ 18}} & = & \frac{-16}{18} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+11}& = & -13 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11-x } & = & -13 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -13 \color{blue}{-11} \\\Leftrightarrow &3x & = &-24\\\Leftrightarrow & \color{red}{3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-24}{3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+11}& = & 3 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+11}\color{blue}{-11-3x } & = & 3 \color{red}{ +3x }\color{blue}{-11-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 3 \color{blue}{-11} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)