Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{-1}& = & 8 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{-1}\color{blue}{+1-9x } & = & 8 \color{red}{ +9x }\color{blue}{+1-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & 8 \color{blue}{+1} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-9}& = & -5 \color{red}{ +x } \\\Leftrightarrow & 11x \color{red}{-9}\color{blue}{+9-x } & = & -5 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 11x \color{blue}{-x } & = & -5 \color{blue}{+9} \\\Leftrightarrow &10x & = &4\\\Leftrightarrow & \color{red}{10}x & = &4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}{ 10}} & = & \frac{4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+4}& = & -13 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4-5x } & = & -13 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -13 \color{blue}{-4} \\\Leftrightarrow &-17x & = &-17\\\Leftrightarrow & \color{red}{-17}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-17}{-17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-9}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9-x } & = & -1 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{+9} \\\Leftrightarrow &-11x & = &8\\\Leftrightarrow & \color{red}{-11}x & = &8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{11} } & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+8}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+8}\color{blue}{-8-x } & = & -13 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &-9x & = &-21\\\Leftrightarrow & \color{red}{-9}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-5}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5-x } & = & -5 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-3}& = & -9 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+3x } & = & -9 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & -9 \color{blue}{+3} \\\Leftrightarrow &16x & = &-6\\\Leftrightarrow & \color{red}{16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{-6}{16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{+14}& = & -12 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14-2x } & = & -12 \color{red}{ +2x }\color{blue}{-14-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -12 \color{blue}{-14} \\\Leftrightarrow &3x & = &-26\\\Leftrightarrow & \color{red}{3}x & = &-26\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-26}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+1}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+1}\color{blue}{-1-x } & = & -5 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{+12}& = & 13 \color{red}{ -13x } \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12+13x } & = & 13 \color{red}{ -13x }\color{blue}{-12+13x } \\\Leftrightarrow & 10x \color{blue}{+13x } & = & 13 \color{blue}{-12} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-15}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-15}\color{blue}{+15-x } & = & -15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -15 \color{blue}{+15} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2-x } & = & -3 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -3 \color{blue}{+2} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)