Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+2}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & -7 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -7 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-12}& = & 10 \color{red}{ +3x } \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12-3x } & = & 10 \color{red}{ +3x }\color{blue}{+12-3x } \\\Leftrightarrow & -5x \color{blue}{-3x } & = & 10 \color{blue}{+12} \\\Leftrightarrow &-8x & = &22\\\Leftrightarrow & \color{red}{-8}x & = &22\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{22}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+5}& = & 11 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{+5}\color{blue}{-5-13x } & = & 11 \color{red}{ +13x }\color{blue}{-5-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 11 \color{blue}{-5} \\\Leftrightarrow &-18x & = &6\\\Leftrightarrow & \color{red}{-18}x & = &6\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{6}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{-7}& = & -1 \color{red}{ +4x } \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7-4x } & = & -1 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 9x \color{blue}{-4x } & = & -1 \color{blue}{+7} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+4}& = & -6 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4-x } & = & -6 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -6 \color{blue}{-4} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+8}& = & 4 \color{red}{ -13x } \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8+13x } & = & 4 \color{red}{ -13x }\color{blue}{-8+13x } \\\Leftrightarrow & 11x \color{blue}{+13x } & = & 4 \color{blue}{-8} \\\Leftrightarrow &24x & = &-4\\\Leftrightarrow & \color{red}{24}x & = &-4\\\Leftrightarrow & \frac{\color{red}{24}x}{ \color{blue}{ 24}} & = & \frac{-4}{24} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -9x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-10x & = &-16\\\Leftrightarrow & \color{red}{-10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}{ -10}} & = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+2}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & -5 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & -5 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-4}& = & 11 \color{red}{ +4x } \\\Leftrightarrow & -11x \color{red}{-4}\color{blue}{+4-4x } & = & 11 \color{red}{ +4x }\color{blue}{+4-4x } \\\Leftrightarrow & -11x \color{blue}{-4x } & = & 11 \color{blue}{+4} \\\Leftrightarrow &-15x & = &15\\\Leftrightarrow & \color{red}{-15}x & = &15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{15}{-15} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-8}& = & 13 \color{red}{ -3x } \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8+3x } & = & 13 \color{red}{ -3x }\color{blue}{+8+3x } \\\Leftrightarrow & 13x \color{blue}{+3x } & = & 13 \color{blue}{+8} \\\Leftrightarrow &16x & = &21\\\Leftrightarrow & \color{red}{16}x & = &21\\\Leftrightarrow & \frac{\color{red}{16}x}{ \color{blue}{ 16}} & = & \frac{21}{16} \\\Leftrightarrow & \color{green}{ x = \frac{21}{16} } & & \\ & V = \left\{ \frac{21}{16} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+7}& = & 5 \color{red}{ -10x } \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7+10x } & = & 5 \color{red}{ -10x }\color{blue}{-7+10x } \\\Leftrightarrow & -x \color{blue}{+10x } & = & 5 \color{blue}{-7} \\\Leftrightarrow &9x & = &-2\\\Leftrightarrow & \color{red}{9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{-2}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{9} } & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+9}& = & 2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9-x } & = & 2 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 2 \color{blue}{-9} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)