Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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