Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+10}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10-x } & = & 14 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 14 \color{blue}{-10} \\\Leftrightarrow &-16x & = &4\\\Leftrightarrow & \color{red}{-16}x & = &4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{-5}& = & -3 \color{red}{ +13x } \\\Leftrightarrow & 3x \color{red}{-5}\color{blue}{+5-13x } & = & -3 \color{red}{ +13x }\color{blue}{+5-13x } \\\Leftrightarrow & 3x \color{blue}{-13x } & = & -3 \color{blue}{+5} \\\Leftrightarrow &-10x & = &2\\\Leftrightarrow & \color{red}{-10}x & = &2\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{2}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+3}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3+7x } & = & -2 \color{red}{ -7x }\color{blue}{-3+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -2 \color{blue}{-3} \\\Leftrightarrow &11x & = &-5\\\Leftrightarrow & \color{red}{11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{-5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-8}& = & -15 \color{red}{ +4x } \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8-4x } & = & -15 \color{red}{ +4x }\color{blue}{+8-4x } \\\Leftrightarrow & -3x \color{blue}{-4x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+4}& = & 1 \color{red}{ -4x } \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4+4x } & = & 1 \color{red}{ -4x }\color{blue}{-4+4x } \\\Leftrightarrow & 9x \color{blue}{+4x } & = & 1 \color{blue}{-4} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{+9}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9-x } & = & 8 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 8 \color{blue}{-9} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{-9}& = & 15 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-x } & = & 15 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & 15 \color{blue}{+9} \\\Leftrightarrow &7x & = &24\\\Leftrightarrow & \color{red}{7}x & = &24\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{24}{7} \\\Leftrightarrow & \color{green}{ x = \frac{24}{7} } & & \\ & V = \left\{ \frac{24}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+6}& = & 2 \color{red}{ +12x } \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6-12x } & = & 2 \color{red}{ +12x }\color{blue}{-6-12x } \\\Leftrightarrow & -11x \color{blue}{-12x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &-23x & = &-4\\\Leftrightarrow & \color{red}{-23}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{-4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{4}{23} } & & \\ & V = \left\{ \frac{4}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-9}& = & -2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{-9}\color{blue}{+9-5x } & = & -2 \color{red}{ +5x }\color{blue}{+9-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &-9x & = &7\\\Leftrightarrow & \color{red}{-9}x & = &7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{9} } & & \\ & V = \left\{ \frac{-7}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-4}& = & 4 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-4}\color{blue}{+4-13x } & = & 4 \color{red}{ +13x }\color{blue}{+4-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 4 \color{blue}{+4} \\\Leftrightarrow &-28x & = &8\\\Leftrightarrow & \color{red}{-28}x & = &8\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{8}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+15}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15-13x } & = & 5 \color{red}{ +13x }\color{blue}{-15-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 5 \color{blue}{-15} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-9}& = & -3 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9-x } & = & -3 \color{red}{ +x }\color{blue}{+9-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -3 \color{blue}{+9} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)