Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-14}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & 15 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 15 \color{blue}{+14} \\\Leftrightarrow &-15x & = &29\\\Leftrightarrow & \color{red}{-15}x & = &29\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{29}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{15} } & & \\ & V = \left\{ \frac{-29}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{-4}& = & 7 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{-4}\color{blue}{+4+2x } & = & 7 \color{red}{ -2x }\color{blue}{+4+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 7 \color{blue}{+4} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{-1}& = & 6 \color{red}{ -3x } \\\Leftrightarrow & 10x \color{red}{-1}\color{blue}{+1+3x } & = & 6 \color{red}{ -3x }\color{blue}{+1+3x } \\\Leftrightarrow & 10x \color{blue}{+3x } & = & 6 \color{blue}{+1} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-10}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10-x } & = & 11 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 11 \color{blue}{+10} \\\Leftrightarrow &-13x & = &21\\\Leftrightarrow & \color{red}{-13}x & = &21\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{21}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{13} } & & \\ & V = \left\{ \frac{-21}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-8}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8-x } & = & -15 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & -15 \color{blue}{+8} \\\Leftrightarrow &-8x & = &-7\\\Leftrightarrow & \color{red}{-8}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-7}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-10}& = & 14 \color{red}{ +13x } \\\Leftrightarrow & -15x \color{red}{-10}\color{blue}{+10-13x } & = & 14 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & -15x \color{blue}{-13x } & = & 14 \color{blue}{+10} \\\Leftrightarrow &-28x & = &24\\\Leftrightarrow & \color{red}{-28}x & = &24\\\Leftrightarrow & \frac{\color{red}{-28}x}{ \color{blue}{ -28}} & = & \frac{24}{-28} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+9}& = & 2 \color{red}{ +5x } \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9-5x } & = & 2 \color{red}{ +5x }\color{blue}{-9-5x } \\\Leftrightarrow & -4x \color{blue}{-5x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+10}& = & -15 \color{red}{ +3x } \\\Leftrightarrow & 8x \color{red}{+10}\color{blue}{-10-3x } & = & -15 \color{red}{ +3x }\color{blue}{-10-3x } \\\Leftrightarrow & 8x \color{blue}{-3x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &5x & = &-25\\\Leftrightarrow & \color{red}{5}x & = &-25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-25}{5} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-10}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-10}\color{blue}{+10-x } & = & 6 \color{red}{ +x }\color{blue}{+10-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 6 \color{blue}{+10} \\\Leftrightarrow &-14x & = &16\\\Leftrightarrow & \color{red}{-14}x & = &16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-8}& = & -14 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8-x } & = & -14 \color{red}{ +x }\color{blue}{+8-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -14 \color{blue}{+8} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+3}& = & -5 \color{red}{ +7x } \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3-7x } & = & -5 \color{red}{ +7x }\color{blue}{-3-7x } \\\Leftrightarrow & 4x \color{blue}{-7x } & = & -5 \color{blue}{-3} \\\Leftrightarrow &-3x & = &-8\\\Leftrightarrow & \color{red}{-3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-10}& = & -7 \color{red}{ +13x } \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10-13x } & = & -7 \color{red}{ +13x }\color{blue}{+10-13x } \\\Leftrightarrow & 11x \color{blue}{-13x } & = & -7 \color{blue}{+10} \\\Leftrightarrow &-2x & = &3\\\Leftrightarrow & \color{red}{-2}x & = &3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}{ -2}} & = & \frac{3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)