Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+4}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4+6x } & = & -1 \color{red}{ -6x }\color{blue}{-4+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &19x & = &-5\\\Leftrightarrow & \color{red}{19}x & = &-5\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-5}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{19} } & & \\ & V = \left\{ \frac{-5}{19} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+6}& = & 2 \color{red}{ -10x } \\\Leftrightarrow & 7x \color{red}{+6}\color{blue}{-6+10x } & = & 2 \color{red}{ -10x }\color{blue}{-6+10x } \\\Leftrightarrow & 7x \color{blue}{+10x } & = & 2 \color{blue}{-6} \\\Leftrightarrow &17x & = &-4\\\Leftrightarrow & \color{red}{17}x & = &-4\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-4}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{17} } & & \\ & V = \left\{ \frac{-4}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-15}& = & -3 \color{red}{ +11x } \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15-11x } & = & -3 \color{red}{ +11x }\color{blue}{+15-11x } \\\Leftrightarrow & -7x \color{blue}{-11x } & = & -3 \color{blue}{+15} \\\Leftrightarrow &-18x & = &12\\\Leftrightarrow & \color{red}{-18}x & = &12\\\Leftrightarrow & \frac{\color{red}{-18}x}{ \color{blue}{ -18}} & = & \frac{12}{-18} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+4}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+4}\color{blue}{-4-x } & = & 10 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 10 \color{blue}{-4} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+1}& = & 2 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1-7x } & = & 2 \color{red}{ +7x }\color{blue}{-1-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 2 \color{blue}{-1} \\\Leftrightarrow &-17x & = &1\\\Leftrightarrow & \color{red}{-17}x & = &1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{17} } & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{+4}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+4}\color{blue}{-4-x } & = & -7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & -7 \color{blue}{-4} \\\Leftrightarrow &-9x & = &-11\\\Leftrightarrow & \color{red}{-9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-14}& = & 9 \color{red}{ +13x } \\\Leftrightarrow & 14x \color{red}{-14}\color{blue}{+14-13x } & = & 9 \color{red}{ +13x }\color{blue}{+14-13x } \\\Leftrightarrow & 14x \color{blue}{-13x } & = & 9 \color{blue}{+14} \\\Leftrightarrow &x & = &23\\\Leftrightarrow & \color{red}{}x & = &23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 23 \\\Leftrightarrow & \color{green}{ x = 23 } & & \\ & V = \left\{ 23 \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-7}& = & 15 \color{red}{ +4x } \\\Leftrightarrow & 7x \color{red}{-7}\color{blue}{+7-4x } & = & 15 \color{red}{ +4x }\color{blue}{+7-4x } \\\Leftrightarrow & 7x \color{blue}{-4x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &3x & = &22\\\Leftrightarrow & \color{red}{3}x & = &22\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{22}{3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+6}& = & 10 \color{red}{ +10x } \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6-10x } & = & 10 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & -9x \color{blue}{-10x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &-19x & = &4\\\Leftrightarrow & \color{red}{-19}x & = &4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{19} } & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+1}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1-x } & = & -15 \color{red}{ +x }\color{blue}{-1-x } \\\Leftrightarrow & 9x \color{blue}{-x } & = & -15 \color{blue}{-1} \\\Leftrightarrow &8x & = &-16\\\Leftrightarrow & \color{red}{8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-16}{8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+13}& = & 14 \color{red}{ +12x } \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13-12x } & = & 14 \color{red}{ +12x }\color{blue}{-13-12x } \\\Leftrightarrow & 11x \color{blue}{-12x } & = & 14 \color{blue}{-13} \\\Leftrightarrow &-x & = &1\\\Leftrightarrow & \color{red}{-}x & = &1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{1}{-1} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{-5}& = & 11 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5-x } & = & 11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 11 \color{blue}{+5} \\\Leftrightarrow &-6x & = &16\\\Leftrightarrow & \color{red}{-6}x & = &16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)