Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+5}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5-4x } & = & 11 \color{red}{ +4x }\color{blue}{-5-4x } \\\Leftrightarrow & -7x \color{blue}{-4x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-1}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-x } & = & -12 \color{red}{ +x }\color{blue}{+1-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -12 \color{blue}{+1} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{+3}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3+6x } & = & -12 \color{red}{ -6x }\color{blue}{-3+6x } \\\Leftrightarrow & 7x \color{blue}{+6x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-2}& = & -6 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-8x } & = & -6 \color{red}{ +8x }\color{blue}{+2-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -6 \color{blue}{+2} \\\Leftrightarrow &-23x & = &-4\\\Leftrightarrow & \color{red}{-23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+6}& = & 8 \color{red}{ +8x } \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6-8x } & = & 8 \color{red}{ +8x }\color{blue}{-6-8x } \\\Leftrightarrow & 3x \color{blue}{-8x } & = & 8 \color{blue}{-6} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2-x } & = & 4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 4 \color{blue}{-2} \\\Leftrightarrow &-12x & = &2\\\Leftrightarrow & \color{red}{-12}x & = &2\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{2}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+9}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & 8x \color{red}{+9}\color{blue}{-9-13x } & = & 4 \color{red}{ +13x }\color{blue}{-9-13x } \\\Leftrightarrow & 8x \color{blue}{-13x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-5x & = &-5\\\Leftrightarrow & \color{red}{-5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-5}{-5} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-4}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-13x } & = & 5 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 5 \color{blue}{+4} \\\Leftrightarrow &-28x & = &9\\\Leftrightarrow & \color{red}{-28}x & = &9\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{9}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{28} } & & \\ & V = \left\{ \frac{-9}{28} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+1}& = & 15 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+1}\color{blue}{-1+13x } & = & 15 \color{red}{ -13x }\color{blue}{-1+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 15 \color{blue}{-1} \\\Leftrightarrow &24x & = &14\\\Leftrightarrow & \color{red}{24}x & = &14\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{14}{24} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{+9}& = & -14 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9-11x } & = & -14 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -14 \color{blue}{-9} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-9}& = & 14 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9-x } & = & 14 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & 14 \color{blue}{+9} \\\Leftrightarrow &13x & = &23\\\Leftrightarrow & \color{red}{13}x & = &23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)