Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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