Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-3}& = & -14 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3+10x } & = & -14 \color{red}{ -10x }\color{blue}{+3+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & -14 \color{blue}{+3} \\\Leftrightarrow &17x & = &-11\\\Leftrightarrow & \color{red}{17}x & = &-11\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-11}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{17} } & & \\ & V = \left\{ \frac{-11}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+7}& = & -1 \color{red}{ -3x } \\\Leftrightarrow & 4x \color{red}{+7}\color{blue}{-7+3x } & = & -1 \color{red}{ -3x }\color{blue}{-7+3x } \\\Leftrightarrow & 4x \color{blue}{+3x } & = & -1 \color{blue}{-7} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -4x \color{red}{+9}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-x } & = & 9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 9 \color{blue}{-9} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-14}& = & -12 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14+5x } & = & -12 \color{red}{ -5x }\color{blue}{+14+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -12 \color{blue}{+14} \\\Leftrightarrow &8x & = &2\\\Leftrightarrow & \color{red}{8}x & = &2\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{2}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{-7}& = & -10 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-7}\color{blue}{+7+11x } & = & -10 \color{red}{ -11x }\color{blue}{+7+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -10 \color{blue}{+7} \\\Leftrightarrow &23x & = &-3\\\Leftrightarrow & \color{red}{23}x & = &-3\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-3}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{23} } & & \\ & V = \left\{ \frac{-3}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-13}& = & -7 \color{red}{ -9x } \\\Leftrightarrow & 5x \color{red}{-13}\color{blue}{+13+9x } & = & -7 \color{red}{ -9x }\color{blue}{+13+9x } \\\Leftrightarrow & 5x \color{blue}{+9x } & = & -7 \color{blue}{+13} \\\Leftrightarrow &14x & = &6\\\Leftrightarrow & \color{red}{14}x & = &6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{+11}& = & -8 \color{red}{ +6x } \\\Leftrightarrow & x \color{red}{+11}\color{blue}{-11-6x } & = & -8 \color{red}{ +6x }\color{blue}{-11-6x } \\\Leftrightarrow & x \color{blue}{-6x } & = & -8 \color{blue}{-11} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+5}& = & 9 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5-x } & = & 9 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 9 \color{blue}{-5} \\\Leftrightarrow &-3x & = &4\\\Leftrightarrow & \color{red}{-3}x & = &4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -6x \color{red}{+8}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8-x } & = & 6 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 6 \color{blue}{-8} \\\Leftrightarrow &-7x & = &-2\\\Leftrightarrow & \color{red}{-7}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{-1}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1-10x } & = & 11 \color{red}{ +10x }\color{blue}{+1-10x } \\\Leftrightarrow & -x \color{blue}{-10x } & = & 11 \color{blue}{+1} \\\Leftrightarrow &-11x & = &12\\\Leftrightarrow & \color{red}{-11}x & = &12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{11} } & & \\ & V = \left\{ \frac{-12}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-3}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3-4x } & = & -15 \color{red}{ +4x }\color{blue}{+3-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -15 \color{blue}{+3} \\\Leftrightarrow &-7x & = &-12\\\Leftrightarrow & \color{red}{-7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-12}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-15}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15-x } & = & 15 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 15 \color{blue}{+15} \\\Leftrightarrow &-6x & = &30\\\Leftrightarrow & \color{red}{-6}x & = &30\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{30}{-6} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)