Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-15}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{-15}\color{blue}{+15-11x } & = & -14 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -14 \color{blue}{+15} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-4}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -4 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -4 \color{blue}{+4} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+8}& = & -13 \color{red}{ -9x } \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8+9x } & = & -13 \color{red}{ -9x }\color{blue}{-8+9x } \\\Leftrightarrow & 10x \color{blue}{+9x } & = & -13 \color{blue}{-8} \\\Leftrightarrow &19x & = &-21\\\Leftrightarrow & \color{red}{19}x & = &-21\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-21}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{19} } & & \\ & V = \left\{ \frac{-21}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+8}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8-14x } & = & -3 \color{red}{ +14x }\color{blue}{-8-14x } \\\Leftrightarrow & 3x \color{blue}{-14x } & = & -3 \color{blue}{-8} \\\Leftrightarrow &-11x & = &-11\\\Leftrightarrow & \color{red}{-11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-11}{-11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-12}& = & 9 \color{red}{ -5x } \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12+5x } & = & 9 \color{red}{ -5x }\color{blue}{+12+5x } \\\Leftrightarrow & 6x \color{blue}{+5x } & = & 9 \color{blue}{+12} \\\Leftrightarrow &11x & = &21\\\Leftrightarrow & \color{red}{11}x & = &21\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{21}{11} \\\Leftrightarrow & \color{green}{ x = \frac{21}{11} } & & \\ & V = \left\{ \frac{21}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-12}& = & 6 \color{red}{ +x } \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12-x } & = & 6 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & 4x \color{blue}{-x } & = & 6 \color{blue}{+12} \\\Leftrightarrow &3x & = &18\\\Leftrightarrow & \color{red}{3}x & = &18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{18}{3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{-9}& = & 6 \color{red}{ +10x } \\\Leftrightarrow & -3x \color{red}{-9}\color{blue}{+9-10x } & = & 6 \color{red}{ +10x }\color{blue}{+9-10x } \\\Leftrightarrow & -3x \color{blue}{-10x } & = & 6 \color{blue}{+9} \\\Leftrightarrow &-13x & = &15\\\Leftrightarrow & \color{red}{-13}x & = &15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-7}& = & 12 \color{red}{ -x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7+x } & = & 12 \color{red}{ -x }\color{blue}{+7+x } \\\Leftrightarrow & x \color{blue}{+x } & = & 12 \color{blue}{+7} \\\Leftrightarrow &2x & = &19\\\Leftrightarrow & \color{red}{2}x & = &19\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{19}{2} \\\Leftrightarrow & \color{green}{ x = \frac{19}{2} } & & \\ & V = \left\{ \frac{19}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{+13}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+13}\color{blue}{-13-x } & = & -7 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &x & = &-20\\\Leftrightarrow & \color{red}{}x & = &-20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -20 \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+10}& = & -5 \color{red}{ +13x } \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10-13x } & = & -5 \color{red}{ +13x }\color{blue}{-10-13x } \\\Leftrightarrow & -12x \color{blue}{-13x } & = & -5 \color{blue}{-10} \\\Leftrightarrow &-25x & = &-15\\\Leftrightarrow & \color{red}{-25}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-15}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-1}& = & -15 \color{red}{ +5x } \\\Leftrightarrow & -2x \color{red}{-1}\color{blue}{+1-5x } & = & -15 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -2x \color{blue}{-5x } & = & -15 \color{blue}{+1} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+4}& = & -10 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4-7x } & = & -10 \color{red}{ +7x }\color{blue}{-4-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -10 \color{blue}{-4} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)