Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -14x \color{red}{-7}& = & 5 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-x } & = & 5 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & 5 \color{blue}{+7} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{+12}& = & 8 \color{red}{ +11x } \\\Leftrightarrow & -5x \color{red}{+12}\color{blue}{-12-11x } & = & 8 \color{red}{ +11x }\color{blue}{-12-11x } \\\Leftrightarrow & -5x \color{blue}{-11x } & = & 8 \color{blue}{-12} \\\Leftrightarrow &-16x & = &-4\\\Leftrightarrow & \color{red}{-16}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-4}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+2}& = & -4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2-x } & = & -4 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & -4 \color{blue}{-2} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-11}& = & -10 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11-8x } & = & -10 \color{red}{ +8x }\color{blue}{+11-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -10 \color{blue}{+11} \\\Leftrightarrow &-23x & = &1\\\Leftrightarrow & \color{red}{-23}x & = &1\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{1}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{23} } & & \\ & V = \left\{ \frac{-1}{23} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+10}& = & -15 \color{red}{ +x } \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10-x } & = & -15 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & 14x \color{blue}{-x } & = & -15 \color{blue}{-10} \\\Leftrightarrow &13x & = &-25\\\Leftrightarrow & \color{red}{13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-1}& = & -6 \color{red}{ +10x } \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1-10x } & = & -6 \color{red}{ +10x }\color{blue}{+1-10x } \\\Leftrightarrow & 7x \color{blue}{-10x } & = & -6 \color{blue}{+1} \\\Leftrightarrow &-3x & = &-5\\\Leftrightarrow & \color{red}{-3}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}{ -3}} & = & \frac{-5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-11}& = & -2 \color{red}{ -2x } \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11+2x } & = & -2 \color{red}{ -2x }\color{blue}{+11+2x } \\\Leftrightarrow & 5x \color{blue}{+2x } & = & -2 \color{blue}{+11} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+4}& = & -11 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4-14x } & = & -11 \color{red}{ +14x }\color{blue}{-4-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -11 \color{blue}{-4} \\\Leftrightarrow &-25x & = &-15\\\Leftrightarrow & \color{red}{-25}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{-15}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+11}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 8x \color{red}{+11}\color{blue}{-11+7x } & = & -14 \color{red}{ -7x }\color{blue}{-11+7x } \\\Leftrightarrow & 8x \color{blue}{+7x } & = & -14 \color{blue}{-11} \\\Leftrightarrow &15x & = &-25\\\Leftrightarrow & \color{red}{15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}{ 15}} & = & \frac{-25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+7}& = & 10 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7-x } & = & 10 \color{red}{ +x }\color{blue}{-7-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & 10 \color{blue}{-7} \\\Leftrightarrow &14x & = &3\\\Leftrightarrow & \color{red}{14}x & = &3\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{3}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-7}& = & -2 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-7}\color{blue}{+7-x } & = & -2 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-7}& = & 15 \color{red}{ +8x } \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7-8x } & = & 15 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & x \color{blue}{-8x } & = & 15 \color{blue}{+7} \\\Leftrightarrow &-7x & = &22\\\Leftrightarrow & \color{red}{-7}x & = &22\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{22}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)