Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-3}& = & -8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3-x } & = & -8 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+6}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6-x } & = & -3 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & -3 \color{blue}{-6} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+14}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{+14}\color{blue}{-14-11x } & = & -14 \color{red}{ +11x }\color{blue}{-14-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -14 \color{blue}{-14} \\\Leftrightarrow &-6x & = &-28\\\Leftrightarrow & \color{red}{-6}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-28}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+10}& = & -2 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{+10}\color{blue}{-10-13x } & = & -2 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -2 \color{blue}{-10} \\\Leftrightarrow &-10x & = &-12\\\Leftrightarrow & \color{red}{-10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-12}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-15}& = & -14 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15+9x } & = & -14 \color{red}{ -9x }\color{blue}{+15+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{-11}& = & 4 \color{red}{ +7x } \\\Leftrightarrow & 10x \color{red}{-11}\color{blue}{+11-7x } & = & 4 \color{red}{ +7x }\color{blue}{+11-7x } \\\Leftrightarrow & 10x \color{blue}{-7x } & = & 4 \color{blue}{+11} \\\Leftrightarrow &3x & = &15\\\Leftrightarrow & \color{red}{3}x & = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+2}& = & -4 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2+3x } & = & -4 \color{red}{ -3x }\color{blue}{-2+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-3}& = & -3 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{-3}\color{blue}{+3+3x } & = & -3 \color{red}{ -3x }\color{blue}{+3+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -3 \color{blue}{+3} \\\Leftrightarrow &7x & = &0\\\Leftrightarrow & \color{red}{7}x & = &0\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{0}{7} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-1}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1-x } & = & -14 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -14 \color{blue}{+1} \\\Leftrightarrow &-14x & = &-13\\\Leftrightarrow & \color{red}{-14}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-13}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{13}{14} } & & \\ & V = \left\{ \frac{13}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-10}& = & 15 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10+4x } & = & 15 \color{red}{ -4x }\color{blue}{+10+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & 15 \color{blue}{+10} \\\Leftrightarrow &3x & = &25\\\Leftrightarrow & \color{red}{3}x & = &25\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{25}{3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)