Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-15x & = &6\\\Leftrightarrow & \color{red}{-15}x & = &6\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{6}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{+12}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12-x } & = & 4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 4 \color{blue}{-12} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-8}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -8x \color{red}{-8}\color{blue}{+8-11x } & = & -3 \color{red}{ +11x }\color{blue}{+8-11x } \\\Leftrightarrow & -8x \color{blue}{-11x } & = & -3 \color{blue}{+8} \\\Leftrightarrow &-19x & = &5\\\Leftrightarrow & \color{red}{-19}x & = &5\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{5}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+14}& = & -2 \color{red}{ +x } \\\Leftrightarrow & 3x \color{red}{+14}\color{blue}{-14-x } & = & -2 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 3x \color{blue}{-x } & = & -2 \color{blue}{-14} \\\Leftrightarrow &2x & = &-16\\\Leftrightarrow & \color{red}{2}x & = &-16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-16}{2} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-11}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11-13x } & = & 5 \color{red}{ +13x }\color{blue}{+11-13x } \\\Leftrightarrow & -5x \color{blue}{-13x } & = & 5 \color{blue}{+11} \\\Leftrightarrow &-18x & = &16\\\Leftrightarrow & \color{red}{-18}x & = &16\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{16}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-2}& = & -8 \color{red}{ +5x } \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2-5x } & = & -8 \color{red}{ +5x }\color{blue}{+2-5x } \\\Leftrightarrow & 12x \color{blue}{-5x } & = & -8 \color{blue}{+2} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{+2}& = & 9 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2-3x } & = & 9 \color{red}{ +3x }\color{blue}{-2-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & 9 \color{blue}{-2} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{-5}& = & 14 \color{red}{ +2x } \\\Leftrightarrow & 13x \color{red}{-5}\color{blue}{+5-2x } & = & 14 \color{red}{ +2x }\color{blue}{+5-2x } \\\Leftrightarrow & 13x \color{blue}{-2x } & = & 14 \color{blue}{+5} \\\Leftrightarrow &11x & = &19\\\Leftrightarrow & \color{red}{11}x & = &19\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{19}{11} \\\Leftrightarrow & \color{green}{ x = \frac{19}{11} } & & \\ & V = \left\{ \frac{19}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+4}& = & -7 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4+4x } & = & -7 \color{red}{ -4x }\color{blue}{-4+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &3x & = &-11\\\Leftrightarrow & \color{red}{3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-11}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{-2}& = & 10 \color{red}{ +14x } \\\Leftrightarrow & 11x \color{red}{-2}\color{blue}{+2-14x } & = & 10 \color{red}{ +14x }\color{blue}{+2-14x } \\\Leftrightarrow & 11x \color{blue}{-14x } & = & 10 \color{blue}{+2} \\\Leftrightarrow &-3x & = &12\\\Leftrightarrow & \color{red}{-3}x & = &12\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{12}{-3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-14}& = & 5 \color{red}{ +13x } \\\Leftrightarrow & -4x \color{red}{-14}\color{blue}{+14-13x } & = & 5 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & -4x \color{blue}{-13x } & = & 5 \color{blue}{+14} \\\Leftrightarrow &-17x & = &19\\\Leftrightarrow & \color{red}{-17}x & = &19\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{19}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{17} } & & \\ & V = \left\{ \frac{-19}{17} \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+12}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12-x } & = & -4 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -2x \color{blue}{-x } & = & -4 \color{blue}{-12} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)