Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-1}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1-x } & = & 15 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 15 \color{blue}{+1} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+9}& = & 2 \color{red}{ +11x } \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9-11x } & = & 2 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 6x \color{blue}{-11x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-7\\\Leftrightarrow & \color{red}{-5}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-7}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+12}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12-4x } & = & 11 \color{red}{ +4x }\color{blue}{-12-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & 11 \color{blue}{-12} \\\Leftrightarrow &-19x & = &-1\\\Leftrightarrow & \color{red}{-19}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-1}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{1}{19} } & & \\ & V = \left\{ \frac{1}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+6}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{+6}\color{blue}{-6-x } & = & -14 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -14 \color{blue}{-6} \\\Leftrightarrow &-11x & = &-20\\\Leftrightarrow & \color{red}{-11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{-20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{20}{11} } & & \\ & V = \left\{ \frac{20}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+3}& = & 3 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3-x } & = & 3 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & 3 \color{blue}{-3} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{-6}& = & 3 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{-6}\color{blue}{+6-x } & = & 3 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 3 \color{blue}{+6} \\\Leftrightarrow &14x & = &9\\\Leftrightarrow & \color{red}{14}x & = &9\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{9}{14} \\\Leftrightarrow & \color{green}{ x = \frac{9}{14} } & & \\ & V = \left\{ \frac{9}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-4}& = & 13 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4+4x } & = & 13 \color{red}{ -4x }\color{blue}{+4+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 13 \color{blue}{+4} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-4}& = & 4 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-12x } & = & 4 \color{red}{ +12x }\color{blue}{+4-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-23x & = &8\\\Leftrightarrow & \color{red}{-23}x & = &8\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{8}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{23} } & & \\ & V = \left\{ \frac{-8}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+1}& = & 1 \color{red}{ +8x } \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1-8x } & = & 1 \color{red}{ +8x }\color{blue}{-1-8x } \\\Leftrightarrow & -7x \color{blue}{-8x } & = & 1 \color{blue}{-1} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+7}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+7}\color{blue}{-7-x } & = & 14 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 14 \color{blue}{-7} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)