Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-11}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-x } & = & 9 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 9 \color{blue}{+11} \\\Leftrightarrow &-6x & = &20\\\Leftrightarrow & \color{red}{-6}x & = &20\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{20}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+11}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11+11x } & = & -14 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &14x & = &-25\\\Leftrightarrow & \color{red}{14}x & = &-25\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-25}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{14} } & & \\ & V = \left\{ \frac{-25}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+9}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{+9}\color{blue}{-9+2x } & = & 2 \color{red}{ -2x }\color{blue}{-9+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &5x & = &-7\\\Leftrightarrow & \color{red}{5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+10}& = & -4 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10-x } & = & -4 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & -4 \color{blue}{-10} \\\Leftrightarrow &3x & = &-14\\\Leftrightarrow & \color{red}{3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-14}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{3} } & & \\ & V = \left\{ \frac{-14}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-7}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7-x } & = & 15 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+12}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+12}\color{blue}{-12-x } & = & 7 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 7 \color{blue}{-12} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{-5}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & -2 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -2 \color{blue}{+5} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-2}& = & -11 \color{red}{ +11x } \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2-11x } & = & -11 \color{red}{ +11x }\color{blue}{+2-11x } \\\Leftrightarrow & -10x \color{blue}{-11x } & = & -11 \color{blue}{+2} \\\Leftrightarrow &-21x & = &-9\\\Leftrightarrow & \color{red}{-21}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-9}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+12}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-x } & = & -13 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &-6x & = &-25\\\Leftrightarrow & \color{red}{-6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+2}& = & 9 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+11x } & = & 9 \color{red}{ -11x }\color{blue}{-2+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-8}& = & -15 \color{red}{ -4x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+4x } & = & -15 \color{red}{ -4x }\color{blue}{+8+4x } \\\Leftrightarrow & 13x \color{blue}{+4x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &17x & = &-7\\\Leftrightarrow & \color{red}{17}x & = &-7\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-7}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{17} } & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+7}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 6 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)