Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+6}& = & 9 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6+2x } & = & 9 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 9 \color{blue}{-6} \\\Leftrightarrow &17x & = &3\\\Leftrightarrow & \color{red}{17}x & = &3\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{3}{17} \\\Leftrightarrow & \color{green}{ x = \frac{3}{17} } & & \\ & V = \left\{ \frac{3}{17} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+3}& = & -1 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+3}\color{blue}{-3-8x } & = & -1 \color{red}{ +8x }\color{blue}{-3-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &-15x & = &-4\\\Leftrightarrow & \color{red}{-15}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-4}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{15} } & & \\ & V = \left\{ \frac{4}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-9}& = & 12 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-14x } & = & 12 \color{red}{ +14x }\color{blue}{+9-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & 12 \color{blue}{+9} \\\Leftrightarrow &-27x & = &21\\\Leftrightarrow & \color{red}{-27}x & = &21\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{21}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+3}& = & 5 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3-3x } & = & 5 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & 5 \color{blue}{-3} \\\Leftrightarrow &5x & = &2\\\Leftrightarrow & \color{red}{5}x & = &2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-8}& = & -8 \color{red}{ +7x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-7x } & = & -8 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & -2x \color{blue}{-7x } & = & -8 \color{blue}{+8} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+12}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & -5 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-17\\\Leftrightarrow & \color{red}{-4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+13}& = & 12 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{+13}\color{blue}{-13-x } & = & 12 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 12 \color{blue}{-13} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+5}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-x } & = & 14 \color{red}{ +x }\color{blue}{-5-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 14 \color{blue}{-5} \\\Leftrightarrow &-8x & = &9\\\Leftrightarrow & \color{red}{-8}x & = &9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{8} } & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+9}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & -x \color{red}{+9}\color{blue}{-9+13x } & = & 12 \color{red}{ -13x }\color{blue}{-9+13x } \\\Leftrightarrow & -x \color{blue}{+13x } & = & 12 \color{blue}{-9} \\\Leftrightarrow &12x & = &3\\\Leftrightarrow & \color{red}{12}x & = &3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}{ 12}} & = & \frac{3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-7}& = & 15 \color{red}{ +9x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7-9x } & = & 15 \color{red}{ +9x }\color{blue}{+7-9x } \\\Leftrightarrow & 7x \color{blue}{-9x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-2x & = &22\\\Leftrightarrow & \color{red}{-2}x & = &22\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{22}{-2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15-x } & = & -7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-8x & = &-22\\\Leftrightarrow & \color{red}{-8}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-x } & = & -9 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -9 \color{blue}{+9} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)