Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+4}& = & 1 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-14x } & = & 1 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &-27x & = &-3\\\Leftrightarrow & \color{red}{-27}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-3}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+4}& = & 2 \color{red}{ +10x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4-10x } & = & 2 \color{red}{ +10x }\color{blue}{-4-10x } \\\Leftrightarrow & 9x \color{blue}{-10x } & = & 2 \color{blue}{-4} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-7}& = & -1 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7+13x } & = & -1 \color{red}{ -13x }\color{blue}{+7+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &23x & = &6\\\Leftrightarrow & \color{red}{23}x & = &6\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{6}{23} \\\Leftrightarrow & \color{green}{ x = \frac{6}{23} } & & \\ & V = \left\{ \frac{6}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+13}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13-x } & = & -15 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -15 \color{blue}{-13} \\\Leftrightarrow &14x & = &-28\\\Leftrightarrow & \color{red}{14}x & = &-28\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-28}{14} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+7}& = & -6 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7+2x } & = & -6 \color{red}{ -2x }\color{blue}{-7+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -6 \color{blue}{-7} \\\Leftrightarrow &17x & = &-13\\\Leftrightarrow & \color{red}{17}x & = &-13\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-13}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{17} } & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{+11}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+11}\color{blue}{-11-x } & = & -8 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+3}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-x } & = & -10 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -10 \color{blue}{-3} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4-x } & = & -4 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{-4} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-6}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6-8x } & = & 3 \color{red}{ +8x }\color{blue}{+6-8x } \\\Leftrightarrow & 13x \color{blue}{-8x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &5x & = &9\\\Leftrightarrow & \color{red}{5}x & = &9\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{9}{5} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-9}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9-x } & = & -10 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -10 \color{blue}{+9} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+12}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12-11x } & = & 11 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & 10x \color{blue}{-11x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-3}& = & -14 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3-4x } & = & -14 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)