Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{-9}& = & -6 \color{red}{ +11x } \\\Leftrightarrow & 9x \color{red}{-9}\color{blue}{+9-11x } & = & -6 \color{red}{ +11x }\color{blue}{+9-11x } \\\Leftrightarrow & 9x \color{blue}{-11x } & = & -6 \color{blue}{+9} \\\Leftrightarrow &-2x & = &3\\\Leftrightarrow & \color{red}{-2}x & = &3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-2}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2-9x } & = & 3 \color{red}{ +9x }\color{blue}{+2-9x } \\\Leftrightarrow & 5x \color{blue}{-9x } & = & 3 \color{blue}{+2} \\\Leftrightarrow &-4x & = &5\\\Leftrightarrow & \color{red}{-4}x & = &5\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{5}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+7}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7-x } & = & 3 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 3 \color{blue}{-7} \\\Leftrightarrow &11x & = &-4\\\Leftrightarrow & \color{red}{11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-4}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+3}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & 15x \color{red}{+3}\color{blue}{-3-14x } & = & 10 \color{red}{ +14x }\color{blue}{-3-14x } \\\Leftrightarrow & 15x \color{blue}{-14x } & = & 10 \color{blue}{-3} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+5}& = & 12 \color{red}{ +10x } \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5-10x } & = & 12 \color{red}{ +10x }\color{blue}{-5-10x } \\\Leftrightarrow & 3x \color{blue}{-10x } & = & 12 \color{blue}{-5} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{-11}& = & -2 \color{red}{ +11x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11-11x } & = & -2 \color{red}{ +11x }\color{blue}{+11-11x } \\\Leftrightarrow & 5x \color{blue}{-11x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &-6x & = &9\\\Leftrightarrow & \color{red}{-6}x & = &9\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{9}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+12}& = & -14 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12-8x } & = & -14 \color{red}{ +8x }\color{blue}{-12-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & -14 \color{blue}{-12} \\\Leftrightarrow &-5x & = &-26\\\Leftrightarrow & \color{red}{-5}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-26}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{26}{5} } & & \\ & V = \left\{ \frac{26}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+8}& = & -1 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8-12x } & = & -1 \color{red}{ +12x }\color{blue}{-8-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &-23x & = &-9\\\Leftrightarrow & \color{red}{-23}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-9}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-4}& = & -2 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{-4}\color{blue}{+4-6x } & = & -2 \color{red}{ +6x }\color{blue}{+4-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & -2 \color{blue}{+4} \\\Leftrightarrow &-11x & = &2\\\Leftrightarrow & \color{red}{-11}x & = &2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{11} } & & \\ & V = \left\{ \frac{-2}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{+10}& = & 5 \color{red}{ -9x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10+9x } & = & 5 \color{red}{ -9x }\color{blue}{-10+9x } \\\Leftrightarrow & 14x \color{blue}{+9x } & = & 5 \color{blue}{-10} \\\Leftrightarrow &23x & = &-5\\\Leftrightarrow & \color{red}{23}x & = &-5\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{-5}{23} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{23} } & & \\ & V = \left\{ \frac{-5}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{+6}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+13x } & = & 4 \color{red}{ -13x }\color{blue}{-6+13x } \\\Leftrightarrow & 7x \color{blue}{+13x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &20x & = &-2\\\Leftrightarrow & \color{red}{20}x & = &-2\\\Leftrightarrow & \frac{\color{red}{20}x}{ \color{blue}{ 20}} & = & \frac{-2}{20} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+4}& = & 13 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4+10x } & = & 13 \color{red}{ -10x }\color{blue}{-4+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &17x & = &9\\\Leftrightarrow & \color{red}{17}x & = &9\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{9}{17} \\\Leftrightarrow & \color{green}{ x = \frac{9}{17} } & & \\ & V = \left\{ \frac{9}{17} \right\} & \\\end{align}\)