Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-8}& = & -14 \color{red}{ +7x } \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8-7x } & = & -14 \color{red}{ +7x }\color{blue}{+8-7x } \\\Leftrightarrow & 15x \color{blue}{-7x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &8x & = &-6\\\Leftrightarrow & \color{red}{8}x & = &-6\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-6}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+3}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3-3x } & = & 9 \color{red}{ +3x }\color{blue}{-3-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 9 \color{blue}{-3} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+1}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1-x } & = & 2 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{-9}& = & -7 \color{red}{ +2x } \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9-2x } & = & -7 \color{red}{ +2x }\color{blue}{+9-2x } \\\Leftrightarrow & 5x \color{blue}{-2x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{+15}& = & 6 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15+8x } & = & 6 \color{red}{ -8x }\color{blue}{-15+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 6 \color{blue}{-15} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-8}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 12x \color{red}{-8}\color{blue}{+8-x } & = & 10 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & 12x \color{blue}{-x } & = & 10 \color{blue}{+8} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 4x \color{red}{+8}& = & -13 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+11x } & = & -13 \color{red}{ -11x }\color{blue}{-8+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &15x & = &-21\\\Leftrightarrow & \color{red}{15}x & = &-21\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-21}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{-13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-13}\color{blue}{+13-x } & = & 10 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & 10 \color{blue}{+13} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+13}& = & -10 \color{red}{ +9x } \\\Leftrightarrow & -4x \color{red}{+13}\color{blue}{-13-9x } & = & -10 \color{red}{ +9x }\color{blue}{-13-9x } \\\Leftrightarrow & -4x \color{blue}{-9x } & = & -10 \color{blue}{-13} \\\Leftrightarrow &-13x & = &-23\\\Leftrightarrow & \color{red}{-13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-3}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-x } & = & 2 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 2 \color{blue}{+3} \\\Leftrightarrow &-16x & = &5\\\Leftrightarrow & \color{red}{-16}x & = &5\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{5}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{16} } & & \\ & V = \left\{ \frac{-5}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+6}& = & 15 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6+11x } & = & 15 \color{red}{ -11x }\color{blue}{-6+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & 15 \color{blue}{-6} \\\Leftrightarrow &23x & = &9\\\Leftrightarrow & \color{red}{23}x & = &9\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{9}{23} \\\Leftrightarrow & \color{green}{ x = \frac{9}{23} } & & \\ & V = \left\{ \frac{9}{23} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{+7}& = & -13 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7-x } & = & -13 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -13 \color{blue}{-7} \\\Leftrightarrow &-5x & = &-20\\\Leftrightarrow & \color{red}{-5}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-20}{-5} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)