Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-10}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-x } & = & -9 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -9 \color{blue}{+10} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+15}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & -14 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -14 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-29\\\Leftrightarrow & \color{red}{-13}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-29}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{29}{13} } & & \\ & V = \left\{ \frac{29}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -x \color{red}{-2}\color{blue}{+2-x } & = & -5 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -x \color{blue}{-x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &-2x & = &-3\\\Leftrightarrow & \color{red}{-2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{-3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11-x } & = & -12 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -12 \color{blue}{-11} \\\Leftrightarrow &7x & = &-23\\\Leftrightarrow & \color{red}{7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+8}& = & 8 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8+2x } & = & 8 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-1}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & -11 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{-14}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 9x \color{red}{-14}\color{blue}{+14+11x } & = & -10 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 9x \color{blue}{+11x } & = & -10 \color{blue}{+14} \\\Leftrightarrow &20x & = &4\\\Leftrightarrow & \color{red}{20}x & = &4\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{4}{20} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+5}& = & 2 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+5}\color{blue}{-5+3x } & = & 2 \color{red}{ -3x }\color{blue}{-5+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & 2 \color{blue}{-5} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+3}& = & 5 \color{red}{ -7x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3+7x } & = & 5 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 15x \color{blue}{+7x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &22x & = &2\\\Leftrightarrow & \color{red}{22}x & = &2\\\Leftrightarrow & \frac{\color{red}{22}x}{ \color{blue}{ 22}} & = & \frac{2}{22} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-15x & = &-6\\\Leftrightarrow & \color{red}{-15}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-11}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-11}\color{blue}{+11-x } & = & -12 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -12 \color{blue}{+11} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-6}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-6}\color{blue}{+6-x } & = & -13 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -13 \color{blue}{+6} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)