Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & x \color{red}{+7}& = & -15 \color{red}{ -10x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+10x } & = & -15 \color{red}{ -10x }\color{blue}{-7+10x } \\\Leftrightarrow & x \color{blue}{+10x } & = & -15 \color{blue}{-7} \\\Leftrightarrow &11x & = &-22\\\Leftrightarrow & \color{red}{11}x & = &-22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-22}{11} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+3}& = & -4 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+3}\color{blue}{-3+5x } & = & -4 \color{red}{ -5x }\color{blue}{-3+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -4 \color{blue}{-3} \\\Leftrightarrow &8x & = &-7\\\Leftrightarrow & \color{red}{8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{8} } & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+6}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6-x } & = & -9 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -9 \color{blue}{-6} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-12}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12-7x } & = & 12 \color{red}{ +7x }\color{blue}{+12-7x } \\\Leftrightarrow & -13x \color{blue}{-7x } & = & 12 \color{blue}{+12} \\\Leftrightarrow &-20x & = &24\\\Leftrightarrow & \color{red}{-20}x & = &24\\\Leftrightarrow & \frac{\color{red}{-20}x}{ \color{blue}{ -20}} & = & \frac{24}{-20} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+1}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 2x \color{red}{+1}\color{blue}{-1-11x } & = & -4 \color{red}{ +11x }\color{blue}{-1-11x } \\\Leftrightarrow & 2x \color{blue}{-11x } & = & -4 \color{blue}{-1} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-2}& = & 12 \color{red}{ +13x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-13x } & = & 12 \color{red}{ +13x }\color{blue}{+2-13x } \\\Leftrightarrow & -2x \color{blue}{-13x } & = & 12 \color{blue}{+2} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{-11}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11-x } & = & 11 \color{red}{ +x }\color{blue}{+11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 11 \color{blue}{+11} \\\Leftrightarrow &-8x & = &22\\\Leftrightarrow & \color{red}{-8}x & = &22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-10}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{-10}\color{blue}{+10-4x } & = & -15 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & -15 \color{blue}{+10} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+13}& = & 4 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{+13}\color{blue}{-13-3x } & = & 4 \color{red}{ +3x }\color{blue}{-13-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & 4 \color{blue}{-13} \\\Leftrightarrow &7x & = &-9\\\Leftrightarrow & \color{red}{7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-3}& = & 11 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3+2x } & = & 11 \color{red}{ -2x }\color{blue}{+3+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 11 \color{blue}{+3} \\\Leftrightarrow &x & = &14\\\Leftrightarrow & \color{red}{}x & = &14\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 14 \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
11. \(\begin{align} & -5x \color{red}{+13}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13-x } & = & -1 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & -1 \color{blue}{-13} \\\Leftrightarrow &-6x & = &-14\\\Leftrightarrow & \color{red}{-6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{-6}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6-x } & = & 2 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{+6} \\\Leftrightarrow &-8x & = &8\\\Leftrightarrow & \color{red}{-8}x & = &8\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{8}{-8} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)