Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+2}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & -3 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -3 \color{blue}{-2} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-5}& = & -15 \color{red}{ -2x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5+2x } & = & -15 \color{red}{ -2x }\color{blue}{+5+2x } \\\Leftrightarrow & 3x \color{blue}{+2x } & = & -15 \color{blue}{+5} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-2}& = & -10 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2-x } & = & -10 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -10 \color{blue}{+2} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-1}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-x } & = & -1 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -1 \color{blue}{+1} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-12}& = & 2 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12+2x } & = & 2 \color{red}{ -2x }\color{blue}{+12+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &17x & = &14\\\Leftrightarrow & \color{red}{17}x & = &14\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{14}{17} \\\Leftrightarrow & \color{green}{ x = \frac{14}{17} } & & \\ & V = \left\{ \frac{14}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+8}& = & -1 \color{red}{ -15x } \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8+15x } & = & -1 \color{red}{ -15x }\color{blue}{-8+15x } \\\Leftrightarrow & 4x \color{blue}{+15x } & = & -1 \color{blue}{-8} \\\Leftrightarrow &19x & = &-9\\\Leftrightarrow & \color{red}{19}x & = &-9\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-9}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{19} } & & \\ & V = \left\{ \frac{-9}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-10}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10-x } & = & -3 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -3 \color{blue}{+10} \\\Leftrightarrow &-11x & = &7\\\Leftrightarrow & \color{red}{-11}x & = &7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{11} } & & \\ & V = \left\{ \frac{-7}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{-14}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14-x } & = & -9 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -9 \color{blue}{+14} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-12}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-12}\color{blue}{+12-x } & = & 2 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 2 \color{blue}{+12} \\\Leftrightarrow &-8x & = &14\\\Leftrightarrow & \color{red}{-8}x & = &14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+14}& = & 13 \color{red}{ +4x } \\\Leftrightarrow & 13x \color{red}{+14}\color{blue}{-14-4x } & = & 13 \color{red}{ +4x }\color{blue}{-14-4x } \\\Leftrightarrow & 13x \color{blue}{-4x } & = & 13 \color{blue}{-14} \\\Leftrightarrow &9x & = &-1\\\Leftrightarrow & \color{red}{9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+13}& = & -7 \color{red}{ -11x } \\\Leftrightarrow & 4x \color{red}{+13}\color{blue}{-13+11x } & = & -7 \color{red}{ -11x }\color{blue}{-13+11x } \\\Leftrightarrow & 4x \color{blue}{+11x } & = & -7 \color{blue}{-13} \\\Leftrightarrow &15x & = &-20\\\Leftrightarrow & \color{red}{15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-20}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+1}& = & 3 \color{red}{ +9x } \\\Leftrightarrow & 10x \color{red}{+1}\color{blue}{-1-9x } & = & 3 \color{red}{ +9x }\color{blue}{-1-9x } \\\Leftrightarrow & 10x \color{blue}{-9x } & = & 3 \color{blue}{-1} \\\Leftrightarrow &x & = &2\\\Leftrightarrow & \color{red}{}x & = &2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 2 \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)