Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7-x } & = & 7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{-15}& = & 4 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-15}\color{blue}{+15-14x } & = & 4 \color{red}{ +14x }\color{blue}{+15-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 4 \color{blue}{+15} \\\Leftrightarrow &-27x & = &19\\\Leftrightarrow & \color{red}{-27}x & = &19\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{19}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{27} } & & \\ & V = \left\{ \frac{-19}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+4}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & 6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{-4} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+12}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-11x } & = & -11 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & -11 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-23\\\Leftrightarrow & \color{red}{-16}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-23}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{23}{16} } & & \\ & V = \left\{ \frac{23}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{+14}& = & -10 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14+3x } & = & -10 \color{red}{ -3x }\color{blue}{-14+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & -10 \color{blue}{-14} \\\Leftrightarrow &13x & = &-24\\\Leftrightarrow & \color{red}{13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-5}& = & 6 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5-5x } & = & 6 \color{red}{ +5x }\color{blue}{+5-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & 6 \color{blue}{+5} \\\Leftrightarrow &-14x & = &11\\\Leftrightarrow & \color{red}{-14}x & = &11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-4}& = & 2 \color{red}{ -6x } \\\Leftrightarrow & x \color{red}{-4}\color{blue}{+4+6x } & = & 2 \color{red}{ -6x }\color{blue}{+4+6x } \\\Leftrightarrow & x \color{blue}{+6x } & = & 2 \color{blue}{+4} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+10}& = & 7 \color{red}{ -3x } \\\Leftrightarrow & x \color{red}{+10}\color{blue}{-10+3x } & = & 7 \color{red}{ -3x }\color{blue}{-10+3x } \\\Leftrightarrow & x \color{blue}{+3x } & = & 7 \color{blue}{-10} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{-6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6-x } & = & 2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-4}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-x } & = & -3 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-5}& = & -5 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5+6x } & = & -5 \color{red}{ -6x }\color{blue}{+5+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -5 \color{blue}{+5} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-2}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-8x } & = & -10 \color{red}{ +8x }\color{blue}{+2-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)