Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{+12}& = & -15 \color{red}{ +x } \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12-x } & = & -15 \color{red}{ +x }\color{blue}{-12-x } \\\Leftrightarrow & -3x \color{blue}{-x } & = & -15 \color{blue}{-12} \\\Leftrightarrow &-4x & = &-27\\\Leftrightarrow & \color{red}{-4}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-27}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+11}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11+11x } & = & -15 \color{red}{ -11x }\color{blue}{-11+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -15 \color{blue}{-11} \\\Leftrightarrow &17x & = &-26\\\Leftrightarrow & \color{red}{17}x & = &-26\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{-26}{17} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{17} } & & \\ & V = \left\{ \frac{-26}{17} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-15}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15-x } & = & 1 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -11x \color{blue}{-x } & = & 1 \color{blue}{+15} \\\Leftrightarrow &-12x & = &16\\\Leftrightarrow & \color{red}{-12}x & = &16\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{16}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-14}& = & -14 \color{red}{ -11x } \\\Leftrightarrow & 6x \color{red}{-14}\color{blue}{+14+11x } & = & -14 \color{red}{ -11x }\color{blue}{+14+11x } \\\Leftrightarrow & 6x \color{blue}{+11x } & = & -14 \color{blue}{+14} \\\Leftrightarrow &17x & = &0\\\Leftrightarrow & \color{red}{17}x & = &0\\\Leftrightarrow & \frac{\color{red}{17}x}{ \color{blue}{ 17}} & = & \frac{0}{17} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-7}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7-x } & = & 7 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -5x \color{blue}{-x } & = & 7 \color{blue}{+7} \\\Leftrightarrow &-6x & = &14\\\Leftrightarrow & \color{red}{-6}x & = &14\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}{ -6}} & = & \frac{14}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-4}& = & -1 \color{red}{ +x } \\\Leftrightarrow & -10x \color{red}{-4}\color{blue}{+4-x } & = & -1 \color{red}{ +x }\color{blue}{+4-x } \\\Leftrightarrow & -10x \color{blue}{-x } & = & -1 \color{blue}{+4} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}{ -11}} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+8}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8-x } & = & 14 \color{red}{ +x }\color{blue}{-8-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{-8} \\\Leftrightarrow &-5x & = &6\\\Leftrightarrow & \color{red}{-5}x & = &6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{-9}& = & -12 \color{red}{ +8x } \\\Leftrightarrow & -13x \color{red}{-9}\color{blue}{+9-8x } & = & -12 \color{red}{ +8x }\color{blue}{+9-8x } \\\Leftrightarrow & -13x \color{blue}{-8x } & = & -12 \color{blue}{+9} \\\Leftrightarrow &-21x & = &-3\\\Leftrightarrow & \color{red}{-21}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-21}x}{ \color{blue}{ -21}} & = & \frac{-3}{-21} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{+9}& = & 11 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9-11x } & = & 11 \color{red}{ +11x }\color{blue}{-9-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 11 \color{blue}{-9} \\\Leftrightarrow &-16x & = &2\\\Leftrightarrow & \color{red}{-16}x & = &2\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{2}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{+7}& = & -7 \color{red}{ +7x } \\\Leftrightarrow & 3x \color{red}{+7}\color{blue}{-7-7x } & = & -7 \color{red}{ +7x }\color{blue}{-7-7x } \\\Leftrightarrow & 3x \color{blue}{-7x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &-4x & = &-14\\\Leftrightarrow & \color{red}{-4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}{ -4}} & = & \frac{-14}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-3}& = & -8 \color{red}{ +11x } \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3-11x } & = & -8 \color{red}{ +11x }\color{blue}{+3-11x } \\\Leftrightarrow & -x \color{blue}{-11x } & = & -8 \color{blue}{+3} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}{ -12}} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-10}& = & 12 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10-4x } & = & 12 \color{red}{ +4x }\color{blue}{+10-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 12 \color{blue}{+10} \\\Leftrightarrow &11x & = &22\\\Leftrightarrow & \color{red}{11}x & = &22\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{22}{11} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)