Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+3}& = & -1 \color{red}{ +13x } \\\Leftrightarrow & -3x \color{red}{+3}\color{blue}{-3-13x } & = & -1 \color{red}{ +13x }\color{blue}{-3-13x } \\\Leftrightarrow & -3x \color{blue}{-13x } & = & -1 \color{blue}{-3} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+7}& = & 6 \color{red}{ +7x } \\\Leftrightarrow & -10x \color{red}{+7}\color{blue}{-7-7x } & = & 6 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & -10x \color{blue}{-7x } & = & 6 \color{blue}{-7} \\\Leftrightarrow &-17x & = &-1\\\Leftrightarrow & \color{red}{-17}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-17}x}{ \color{blue}{ -17}} & = & \frac{-1}{-17} \\\Leftrightarrow & \color{green}{ x = \frac{1}{17} } & & \\ & V = \left\{ \frac{1}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{-12}& = & -10 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12+8x } & = & -10 \color{red}{ -8x }\color{blue}{+12+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & -10 \color{blue}{+12} \\\Leftrightarrow &19x & = &2\\\Leftrightarrow & \color{red}{19}x & = &2\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{2}{19} \\\Leftrightarrow & \color{green}{ x = \frac{2}{19} } & & \\ & V = \left\{ \frac{2}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-5}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{-5}\color{blue}{+5-x } & = & -11 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -11 \color{blue}{+5} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-12}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-12}\color{blue}{+12-x } & = & -7 \color{red}{ +x }\color{blue}{+12-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & -7 \color{blue}{+12} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-1}& = & -4 \color{red}{ +11x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-11x } & = & -4 \color{red}{ +11x }\color{blue}{+1-11x } \\\Leftrightarrow & 15x \color{blue}{-11x } & = & -4 \color{blue}{+1} \\\Leftrightarrow &4x & = &-3\\\Leftrightarrow & \color{red}{4}x & = &-3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}{ 4}} & = & \frac{-3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{-13}& = & 15 \color{red}{ -3x } \\\Leftrightarrow & -x \color{red}{-13}\color{blue}{+13+3x } & = & 15 \color{red}{ -3x }\color{blue}{+13+3x } \\\Leftrightarrow & -x \color{blue}{+3x } & = & 15 \color{blue}{+13} \\\Leftrightarrow &2x & = &28\\\Leftrightarrow & \color{red}{2}x & = &28\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{28}{2} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-6}& = & 11 \color{red}{ -12x } \\\Leftrightarrow & 5x \color{red}{-6}\color{blue}{+6+12x } & = & 11 \color{red}{ -12x }\color{blue}{+6+12x } \\\Leftrightarrow & 5x \color{blue}{+12x } & = & 11 \color{blue}{+6} \\\Leftrightarrow &17x & = &17\\\Leftrightarrow & \color{red}{17}x & = &17\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{17}{17} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+1}& = & -12 \color{red}{ -6x } \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1+6x } & = & -12 \color{red}{ -6x }\color{blue}{-1+6x } \\\Leftrightarrow & -x \color{blue}{+6x } & = & -12 \color{blue}{-1} \\\Leftrightarrow &5x & = &-13\\\Leftrightarrow & \color{red}{5}x & = &-13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}{ 5}} & = & \frac{-13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{+4}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4-x } & = & -11 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-6}& = & 7 \color{red}{ +x } \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6-x } & = & 7 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & 10x \color{blue}{-x } & = & 7 \color{blue}{+6} \\\Leftrightarrow &9x & = &13\\\Leftrightarrow & \color{red}{9}x & = &13\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}{ 9}} & = & \frac{13}{9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -4x \color{red}{-5}& = & -9 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5-x } & = & -9 \color{red}{ +x }\color{blue}{+5-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & -9 \color{blue}{+5} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)