Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-8}& = & -11 \color{red}{ +3x } \\\Leftrightarrow & 10x \color{red}{-8}\color{blue}{+8-3x } & = & -11 \color{red}{ +3x }\color{blue}{+8-3x } \\\Leftrightarrow & 10x \color{blue}{-3x } & = & -11 \color{blue}{+8} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-2}& = & -5 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2-5x } & = & -5 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -5 \color{blue}{+2} \\\Leftrightarrow &x & = &-3\\\Leftrightarrow & \color{red}{}x & = &-3\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -3 \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-10}& = & -10 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10-x } & = & -10 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -10 \color{blue}{+10} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-5}& = & -11 \color{red}{ -12x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5+12x } & = & -11 \color{red}{ -12x }\color{blue}{+5+12x } \\\Leftrightarrow & 13x \color{blue}{+12x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &25x & = &-6\\\Leftrightarrow & \color{red}{25}x & = &-6\\\Leftrightarrow & \frac{\color{red}{25}x}{ \color{blue}{ 25}} & = & \frac{-6}{25} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{25} } & & \\ & V = \left\{ \frac{-6}{25} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-15}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & 14x \color{red}{-15}\color{blue}{+15-11x } & = & 11 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 14x \color{blue}{-11x } & = & 11 \color{blue}{+15} \\\Leftrightarrow &3x & = &26\\\Leftrightarrow & \color{red}{3}x & = &26\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{26}{3} \\\Leftrightarrow & \color{green}{ x = \frac{26}{3} } & & \\ & V = \left\{ \frac{26}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+6}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{+6}\color{blue}{-6-x } & = & 5 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 5 \color{blue}{-6} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9-x } & = & 15 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & 15 \color{blue}{-9} \\\Leftrightarrow &-10x & = &6\\\Leftrightarrow & \color{red}{-10}x & = &6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+2}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2+7x } & = & -7 \color{red}{ -7x }\color{blue}{-2+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+15}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15-x } & = & -7 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-22\\\Leftrightarrow & \color{red}{-13}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-22}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{22}{13} } & & \\ & V = \left\{ \frac{22}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+1}& = & 12 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1-7x } & = & 12 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & 12 \color{blue}{-1} \\\Leftrightarrow &-4x & = &11\\\Leftrightarrow & \color{red}{-4}x & = &11\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{11}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+11}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+11}\color{blue}{-11-x } & = & -9 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -9 \color{blue}{-11} \\\Leftrightarrow &-8x & = &-20\\\Leftrightarrow & \color{red}{-8}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+2}& = & 12 \color{red}{ +6x } \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2-6x } & = & 12 \color{red}{ +6x }\color{blue}{-2-6x } \\\Leftrightarrow & -5x \color{blue}{-6x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &-11x & = &10\\\Leftrightarrow & \color{red}{-11}x & = &10\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{10}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{11} } & & \\ & V = \left\{ \frac{-10}{11} \right\} & \\\end{align}\)