Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

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