Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-2}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2-x } & = & 4 \color{red}{ +x }\color{blue}{+2-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{+2} \\\Leftrightarrow &-16x & = &6\\\Leftrightarrow & \color{red}{-16}x & = &6\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{6}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+9}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9-x } & = & 4 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -6x \color{blue}{-x } & = & 4 \color{blue}{-9} \\\Leftrightarrow &-7x & = &-5\\\Leftrightarrow & \color{red}{-7}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+1}& = & 11 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1-10x } & = & 11 \color{red}{ +10x }\color{blue}{-1-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 11 \color{blue}{-1} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-6}& = & -5 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6-x } & = & -5 \color{red}{ +x }\color{blue}{+6-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & -5 \color{blue}{+6} \\\Leftrightarrow &-16x & = &1\\\Leftrightarrow & \color{red}{-16}x & = &1\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{1}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{16} } & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-14}& = & -11 \color{red}{ +x } \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14-x } & = & -11 \color{red}{ +x }\color{blue}{+14-x } \\\Leftrightarrow & -14x \color{blue}{-x } & = & -11 \color{blue}{+14} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}{ -15}} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-7}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7+7x } & = & -2 \color{red}{ -7x }\color{blue}{+7+7x } \\\Leftrightarrow & 4x \color{blue}{+7x } & = & -2 \color{blue}{+7} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+14}& = & -7 \color{red}{ +x } \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14-x } & = & -7 \color{red}{ +x }\color{blue}{-14-x } \\\Leftrightarrow & 15x \color{blue}{-x } & = & -7 \color{blue}{-14} \\\Leftrightarrow &14x & = &-21\\\Leftrightarrow & \color{red}{14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{-4}& = & -14 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4+7x } & = & -14 \color{red}{ -7x }\color{blue}{+4+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -14 \color{blue}{+4} \\\Leftrightarrow &19x & = &-10\\\Leftrightarrow & \color{red}{19}x & = &-10\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{-10}{19} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{19} } & & \\ & V = \left\{ \frac{-10}{19} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+2}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{+2}\color{blue}{-2-x } & = & 1 \color{red}{ +x }\color{blue}{-2-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{-2} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{+14}& = & -11 \color{red}{ +5x } \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14-5x } & = & -11 \color{red}{ +5x }\color{blue}{-14-5x } \\\Leftrightarrow & 6x \color{blue}{-5x } & = & -11 \color{blue}{-14} \\\Leftrightarrow &x & = &-25\\\Leftrightarrow & \color{red}{}x & = &-25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -25 \\\Leftrightarrow & \color{green}{ x = -25 } & & \\ & V = \left\{ -25 \right\} & \\\end{align}\)
11. \(\begin{align} & -8x \color{red}{+10}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10-x } & = & 4 \color{red}{ +x }\color{blue}{-10-x } \\\Leftrightarrow & -8x \color{blue}{-x } & = & 4 \color{blue}{-10} \\\Leftrightarrow &-9x & = &-6\\\Leftrightarrow & \color{red}{-9}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}{ -9}} & = & \frac{-6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-13}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13-x } & = & 7 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & 7 \color{blue}{+13} \\\Leftrightarrow &-14x & = &20\\\Leftrightarrow & \color{red}{-14}x & = &20\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{20}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)