Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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