Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-10}& = & -1 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-14x } & = & -1 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -1 \color{blue}{+10} \\\Leftrightarrow &-27x & = &9\\\Leftrightarrow & \color{red}{-27}x & = &9\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{9}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+12}& = & -13 \color{red}{ -5x } \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12+5x } & = & -13 \color{red}{ -5x }\color{blue}{-12+5x } \\\Leftrightarrow & 3x \color{blue}{+5x } & = & -13 \color{blue}{-12} \\\Leftrightarrow &8x & = &-25\\\Leftrightarrow & \color{red}{8}x & = &-25\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-25}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{8} } & & \\ & V = \left\{ \frac{-25}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-5}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5-4x } & = & 11 \color{red}{ +4x }\color{blue}{+5-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-19x & = &16\\\Leftrightarrow & \color{red}{-19}x & = &16\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{16}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{19} } & & \\ & V = \left\{ \frac{-16}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-15}& = & -12 \color{red}{ +7x } \\\Leftrightarrow & 9x \color{red}{-15}\color{blue}{+15-7x } & = & -12 \color{red}{ +7x }\color{blue}{+15-7x } \\\Leftrightarrow & 9x \color{blue}{-7x } & = & -12 \color{blue}{+15} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-12}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12-x } & = & -9 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -9 \color{blue}{+12} \\\Leftrightarrow &-4x & = &3\\\Leftrightarrow & \color{red}{-4}x & = &3\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{3}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{+9}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & -9 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-18\\\Leftrightarrow & \color{red}{-7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-18}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{18}{7} } & & \\ & V = \left\{ \frac{18}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-5}& = & 5 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5+15x } & = & 5 \color{red}{ -15x }\color{blue}{+5+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 5 \color{blue}{+5} \\\Leftrightarrow &23x & = &10\\\Leftrightarrow & \color{red}{23}x & = &10\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{10}{23} \\\Leftrightarrow & \color{green}{ x = \frac{10}{23} } & & \\ & V = \left\{ \frac{10}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-3}& = & -2 \color{red}{ +7x } \\\Leftrightarrow & 12x \color{red}{-3}\color{blue}{+3-7x } & = & -2 \color{red}{ +7x }\color{blue}{+3-7x } \\\Leftrightarrow & 12x \color{blue}{-7x } & = & -2 \color{blue}{+3} \\\Leftrightarrow &5x & = &1\\\Leftrightarrow & \color{red}{5}x & = &1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{+7}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+7}\color{blue}{-7-x } & = & -4 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{-7} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+12}& = & 11 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12+10x } & = & 11 \color{red}{ -10x }\color{blue}{-12+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-12}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12-x } & = & 5 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+12} \\\Leftrightarrow &-15x & = &17\\\Leftrightarrow & \color{red}{-15}x & = &17\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{17}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{15} } & & \\ & V = \left\{ \frac{-17}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+1}& = & -9 \color{red}{ +9x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1-9x } & = & -9 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 11x \color{blue}{-9x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &2x & = &-10\\\Leftrightarrow & \color{red}{2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-10}{2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)