Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+12}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & 15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-12} \\\Leftrightarrow &-10x & = &3\\\Leftrightarrow & \color{red}{-10}x & = &3\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{3}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+12}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12-x } & = & -10 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -10 \color{blue}{-12} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 5x \color{red}{-7}& = & 14 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7+2x } & = & 14 \color{red}{ -2x }\color{blue}{+7+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & 14 \color{blue}{+7} \\\Leftrightarrow &7x & = &21\\\Leftrightarrow & \color{red}{7}x & = &21\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{21}{7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-7}& = & -15 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{-7}\color{blue}{+7-9x } & = & -15 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -15 \color{blue}{+7} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+1}& = & -5 \color{red}{ +9x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-9x } & = & -5 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 4x \color{blue}{-9x } & = & -5 \color{blue}{-1} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+2}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & -12 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -12 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-5}& = & 4 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5-x } & = & 4 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & 4 \color{blue}{+5} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-11}& = & 10 \color{red}{ +8x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-8x } & = & 10 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -5x \color{blue}{-8x } & = & 10 \color{blue}{+11} \\\Leftrightarrow &-13x & = &21\\\Leftrightarrow & \color{red}{-13}x & = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6-x } & = & -9 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{+6} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-14}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-14}\color{blue}{+14-11x } & = & -2 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -2 \color{blue}{+14} \\\Leftrightarrow &-18x & = &12\\\Leftrightarrow & \color{red}{-18}x & = &12\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{12}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+14}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14-11x } & = & -13 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -13 \color{blue}{-14} \\\Leftrightarrow &-18x & = &-27\\\Leftrightarrow & \color{red}{-18}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{-27}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-8}& = & 4 \color{red}{ -15x } \\\Leftrightarrow & -x \color{red}{-8}\color{blue}{+8+15x } & = & 4 \color{red}{ -15x }\color{blue}{+8+15x } \\\Leftrightarrow & -x \color{blue}{+15x } & = & 4 \color{blue}{+8} \\\Leftrightarrow &14x & = &12\\\Leftrightarrow & \color{red}{14}x & = &12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)