Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+11}& = & 4 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+11}\color{blue}{-11-x } & = & 4 \color{red}{ +x }\color{blue}{-11-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 4 \color{blue}{-11} \\\Leftrightarrow &-16x & = &-7\\\Leftrightarrow & \color{red}{-16}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{-7}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{7}{16} } & & \\ & V = \left\{ \frac{7}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+9}& = & -7 \color{red}{ +x } \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9-x } & = & -7 \color{red}{ +x }\color{blue}{-9-x } \\\Leftrightarrow & -13x \color{blue}{-x } & = & -7 \color{blue}{-9} \\\Leftrightarrow &-14x & = &-16\\\Leftrightarrow & \color{red}{-14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}{ -14}} & = & \frac{-16}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{8}{7} } & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-14}& = & -13 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14-11x } & = & -13 \color{red}{ +11x }\color{blue}{+14-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & -13 \color{blue}{+14} \\\Leftrightarrow &-7x & = &1\\\Leftrightarrow & \color{red}{-7}x & = &1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-7}& = & 1 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7-x } & = & 1 \color{red}{ +x }\color{blue}{+7-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 1 \color{blue}{+7} \\\Leftrightarrow &-13x & = &8\\\Leftrightarrow & \color{red}{-13}x & = &8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-15}& = & 8 \color{red}{ +x } \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15-x } & = & 8 \color{red}{ +x }\color{blue}{+15-x } \\\Leftrightarrow & -12x \color{blue}{-x } & = & 8 \color{blue}{+15} \\\Leftrightarrow &-13x & = &23\\\Leftrightarrow & \color{red}{-13}x & = &23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{-13}& = & 14 \color{red}{ +x } \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13-x } & = & 14 \color{red}{ +x }\color{blue}{+13-x } \\\Leftrightarrow & -4x \color{blue}{-x } & = & 14 \color{blue}{+13} \\\Leftrightarrow &-5x & = &27\\\Leftrightarrow & \color{red}{-5}x & = &27\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}{ -5}} & = & \frac{27}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{5} } & & \\ & V = \left\{ \frac{-27}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+6}& = & -12 \color{red}{ +x } \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6-x } & = & -12 \color{red}{ +x }\color{blue}{-6-x } \\\Leftrightarrow & 8x \color{blue}{-x } & = & -12 \color{blue}{-6} \\\Leftrightarrow &7x & = &-18\\\Leftrightarrow & \color{red}{7}x & = &-18\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}{ 7}} & = & \frac{-18}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{7} } & & \\ & V = \left\{ \frac{-18}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-10}& = & -13 \color{red}{ +3x } \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10-3x } & = & -13 \color{red}{ +3x }\color{blue}{+10-3x } \\\Leftrightarrow & 5x \color{blue}{-3x } & = & -13 \color{blue}{+10} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}{ 2}} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-1}& = & 5 \color{red}{ +4x } \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1-4x } & = & 5 \color{red}{ +4x }\color{blue}{+1-4x } \\\Leftrightarrow & 15x \color{blue}{-4x } & = & 5 \color{blue}{+1} \\\Leftrightarrow &11x & = &6\\\Leftrightarrow & \color{red}{11}x & = &6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}{ 11}} & = & \frac{6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-3}& = & 3 \color{red}{ +8x } \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3-8x } & = & 3 \color{red}{ +8x }\color{blue}{+3-8x } \\\Leftrightarrow & 7x \color{blue}{-8x } & = & 3 \color{blue}{+3} \\\Leftrightarrow &-x & = &6\\\Leftrightarrow & \color{red}{-}x & = &6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}{ -1}} & = & \frac{6}{-1} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{+4}& = & 3 \color{red}{ -2x } \\\Leftrightarrow & 11x \color{red}{+4}\color{blue}{-4+2x } & = & 3 \color{red}{ -2x }\color{blue}{-4+2x } \\\Leftrightarrow & 11x \color{blue}{+2x } & = & 3 \color{blue}{-4} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}{ 13}} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{+4}& = & -14 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+4}\color{blue}{-4-x } & = & -14 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -14 \color{blue}{-4} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)