Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-16x & = &-6\\\Leftrightarrow & \color{red}{-16}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{+5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5-x } & = & -1 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -1 \color{blue}{-5} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+5}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & -12 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -12 \color{blue}{-5} \\\Leftrightarrow &-8x & = &-17\\\Leftrightarrow & \color{red}{-8}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+14}& = & 8 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14-10x } & = & 8 \color{red}{ +10x }\color{blue}{-14-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 8 \color{blue}{-14} \\\Leftrightarrow &-13x & = &-6\\\Leftrightarrow & \color{red}{-13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{6}{13} } & & \\ & V = \left\{ \frac{6}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+9}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9-11x } & = & -5 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &4x & = &-14\\\Leftrightarrow & \color{red}{4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+6}& = & 8 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6+7x } & = & 8 \color{red}{ -7x }\color{blue}{-6+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+12}\color{blue}{-12-x } & = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-12x & = &-21\\\Leftrightarrow & \color{red}{-12}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-7}& = & 3 \color{red}{ +4x } \\\Leftrightarrow & 11x \color{red}{-7}\color{blue}{+7-4x } & = & 3 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 11x \color{blue}{-4x } & = & 3 \color{blue}{+7} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-9}& = & 12 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-9}\color{blue}{+9+11x } & = & 12 \color{red}{ -11x }\color{blue}{+9+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &26x & = &21\\\Leftrightarrow & \color{red}{26}x & = &21\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{21}{26} \\\Leftrightarrow & \color{green}{ x = \frac{21}{26} } & & \\ & V = \left\{ \frac{21}{26} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+12}& = & 4 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+11x } & = & 4 \color{red}{ -11x }\color{blue}{-12+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12-x } & = & -9 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -9 \color{blue}{-12} \\\Leftrightarrow &-11x & = &-21\\\Leftrightarrow & \color{red}{-11}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-8}& = & -4 \color{red}{ -7x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+7x } & = & -4 \color{red}{ -7x }\color{blue}{+8+7x } \\\Leftrightarrow & -x \color{blue}{+7x } & = & -4 \color{blue}{+8} \\\Leftrightarrow &6x & = &4\\\Leftrightarrow & \color{red}{6}x & = &4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}{ 6}} & = & \frac{4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)