Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-7}& = & -4 \color{red}{ +14x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-14x } & = & -4 \color{red}{ +14x }\color{blue}{+7-14x } \\\Leftrightarrow & 9x \color{blue}{-14x } & = & -4 \color{blue}{+7} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-4}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4+11x } & = & -13 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -13 \color{blue}{+4} \\\Leftrightarrow &17x & = &-9\\\Leftrightarrow & \color{red}{17}x & = &-9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{17} } & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-15}& = & 4 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15-4x } & = & 4 \color{red}{ +4x }\color{blue}{+15-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-19x & = &19\\\Leftrightarrow & \color{red}{-19}x & = &19\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{19}{-19} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-10}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-x } & = & -1 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{+5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 11 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15-x } & = & 15 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 15 \color{blue}{-15} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-8}& = & 2 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8-8x } & = & 2 \color{red}{ +8x }\color{blue}{+8-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 2 \color{blue}{+8} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+14}& = & -9 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14-7x } & = & -9 \color{red}{ +7x }\color{blue}{-14-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & -9 \color{blue}{-14} \\\Leftrightarrow &3x & = &-23\\\Leftrightarrow & \color{red}{3}x & = &-23\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-23}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{3} } & & \\ & V = \left\{ \frac{-23}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{-1}& = & 3 \color{red}{ +11x } \\\Leftrightarrow & 13x \color{red}{-1}\color{blue}{+1-11x } & = & 3 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 13x \color{blue}{-11x } & = & 3 \color{blue}{+1} \\\Leftrightarrow &2x & = &4\\\Leftrightarrow & \color{red}{2}x & = &4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{4}{2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-11}& = & 9 \color{red}{ -14x } \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11+14x } & = & 9 \color{red}{ -14x }\color{blue}{+11+14x } \\\Leftrightarrow & 3x \color{blue}{+14x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &17x & = &20\\\Leftrightarrow & \color{red}{17}x & = &20\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{20}{17} \\\Leftrightarrow & \color{green}{ x = \frac{20}{17} } & & \\ & V = \left\{ \frac{20}{17} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-3}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3+2x } & = & -2 \color{red}{ -2x }\color{blue}{+3+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &17x & = &1\\\Leftrightarrow & \color{red}{17}x & = &1\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{1}{17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-10}\color{blue}{+10-x } & = & -3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-5x & = &7\\\Leftrightarrow & \color{red}{-5}x & = &7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)