Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-6}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6-x } & = & 8 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 8 \color{blue}{+6} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+11}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11-x } & = & 15 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 15 \color{blue}{-11} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{+11}& = & -14 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11-5x } & = & -14 \color{red}{ +5x }\color{blue}{-11-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &9x & = &-25\\\Leftrightarrow & \color{red}{9}x & = &-25\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-25}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{9} } & & \\ & V = \left\{ \frac{-25}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-x } & = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-2}& = & -1 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2+7x } & = & -1 \color{red}{ -7x }\color{blue}{+2+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -1 \color{blue}{+2} \\\Leftrightarrow &19x & = &1\\\Leftrightarrow & \color{red}{19}x & = &1\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{1}{19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-12}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12-13x } & = & -5 \color{red}{ +13x }\color{blue}{+12-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & -5 \color{blue}{+12} \\\Leftrightarrow &-28x & = &7\\\Leftrightarrow & \color{red}{-28}x & = &7\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{7}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-14}& = & 8 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14+13x } & = & 8 \color{red}{ -13x }\color{blue}{+14+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 8 \color{blue}{+14} \\\Leftrightarrow &12x & = &22\\\Leftrightarrow & \color{red}{12}x & = &22\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{22}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-11}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & -14 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -14 \color{blue}{+11} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+9}& = & -5 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9-11x } & = & -5 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -5 \color{blue}{-9} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+3}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x } & = & 8 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 8 \color{blue}{-3} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{-1}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1-5x } & = & -11 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -12x \color{blue}{-5x } & = & -11 \color{blue}{+1} \\\Leftrightarrow &-17x & = &-10\\\Leftrightarrow & \color{red}{-17}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-10}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{10}{17} } & & \\ & V = \left\{ \frac{10}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-5}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5-x } & = & -1 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -1 \color{blue}{+5} \\\Leftrightarrow &-8x & = &4\\\Leftrightarrow & \color{red}{-8}x & = &4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)