Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+3}& = & -12 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3-x } & = & -12 \color{red}{ +x }\color{blue}{-3-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -12 \color{blue}{-3} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-2}& = & 15 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{-2}\color{blue}{+2-x } & = & 15 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 15 \color{blue}{+2} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{-3}& = & -1 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+6x } & = & -1 \color{red}{ -6x }\color{blue}{+3+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -1 \color{blue}{+3} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-3}& = & 10 \color{red}{ -15x } \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3+15x } & = & 10 \color{red}{ -15x }\color{blue}{+3+15x } \\\Leftrightarrow & 13x \color{blue}{+15x } & = & 10 \color{blue}{+3} \\\Leftrightarrow &28x & = &13\\\Leftrightarrow & \color{red}{28}x & = &13\\\Leftrightarrow & \frac{\color{red}{28}x}{ \color{blue}{ 28}} & = & \frac{13}{28} \\\Leftrightarrow & \color{green}{ x = \frac{13}{28} } & & \\ & V = \left\{ \frac{13}{28} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{-7}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-7}\color{blue}{+7-11x } & = & -8 \color{red}{ +11x }\color{blue}{+7-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -8 \color{blue}{+7} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+13}& = & 13 \color{red}{ +6x } \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13-6x } & = & 13 \color{red}{ +6x }\color{blue}{-13-6x } \\\Leftrightarrow & -11x \color{blue}{-6x } & = & 13 \color{blue}{-13} \\\Leftrightarrow &-17x & = &0\\\Leftrightarrow & \color{red}{-17}x & = &0\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{0}{-17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+8}& = & -4 \color{red}{ -2x } \\\Leftrightarrow & 15x \color{red}{+8}\color{blue}{-8+2x } & = & -4 \color{red}{ -2x }\color{blue}{-8+2x } \\\Leftrightarrow & 15x \color{blue}{+2x } & = & -4 \color{blue}{-8} \\\Leftrightarrow &17x & = &-12\\\Leftrightarrow & \color{red}{17}x & = &-12\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-12}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{17} } & & \\ & V = \left\{ \frac{-12}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & -4x \color{red}{+8}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & 8 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 8 \color{blue}{-8} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-11}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11-5x } & = & 13 \color{red}{ +5x }\color{blue}{+11-5x } \\\Leftrightarrow & 14x \color{blue}{-5x } & = & 13 \color{blue}{+11} \\\Leftrightarrow &9x & = &24\\\Leftrightarrow & \color{red}{9}x & = &24\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{24}{9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -9x \color{red}{-1}& = & -9 \color{red}{ +5x } \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1-5x } & = & -9 \color{red}{ +5x }\color{blue}{+1-5x } \\\Leftrightarrow & -9x \color{blue}{-5x } & = & -9 \color{blue}{+1} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-7}& = & -14 \color{red}{ -6x } \\\Leftrightarrow & 13x \color{red}{-7}\color{blue}{+7+6x } & = & -14 \color{red}{ -6x }\color{blue}{+7+6x } \\\Leftrightarrow & 13x \color{blue}{+6x } & = & -14 \color{blue}{+7} \\\Leftrightarrow &19x & = &-7\\\Leftrightarrow & \color{red}{19}x & = &-7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{19} } & & \\ & V = \left\{ \frac{-7}{19} \right\} & \\\end{align}\)
12. \(\begin{align} & 12x \color{red}{+4}& = & -1 \color{red}{ +11x } \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4-11x } & = & -1 \color{red}{ +11x }\color{blue}{-4-11x } \\\Leftrightarrow & 12x \color{blue}{-11x } & = & -1 \color{blue}{-4} \\\Leftrightarrow &x & = &-5\\\Leftrightarrow & \color{red}{}x & = &-5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -5 \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)