Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+13}& = & 10 \color{red}{ +x } \\\Leftrightarrow & -7x \color{red}{+13}\color{blue}{-13-x } & = & 10 \color{red}{ +x }\color{blue}{-13-x } \\\Leftrightarrow & -7x \color{blue}{-x } & = & 10 \color{blue}{-13} \\\Leftrightarrow &-8x & = &-3\\\Leftrightarrow & \color{red}{-8}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}{ -8}} & = & \frac{-3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+11}& = & -3 \color{red}{ +14x } \\\Leftrightarrow & -13x \color{red}{+11}\color{blue}{-11-14x } & = & -3 \color{red}{ +14x }\color{blue}{-11-14x } \\\Leftrightarrow & -13x \color{blue}{-14x } & = & -3 \color{blue}{-11} \\\Leftrightarrow &-27x & = &-14\\\Leftrightarrow & \color{red}{-27}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-27}x}{ \color{blue}{ -27}} & = & \frac{-14}{-27} \\\Leftrightarrow & \color{green}{ x = \frac{14}{27} } & & \\ & V = \left\{ \frac{14}{27} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+1}& = & -9 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1-3x } & = & -9 \color{red}{ +3x }\color{blue}{-1-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -9 \color{blue}{-1} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-8}& = & 8 \color{red}{ -8x } \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8+8x } & = & 8 \color{red}{ -8x }\color{blue}{+8+8x } \\\Leftrightarrow & 11x \color{blue}{+8x } & = & 8 \color{blue}{+8} \\\Leftrightarrow &19x & = &16\\\Leftrightarrow & \color{red}{19}x & = &16\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{16}{19} \\\Leftrightarrow & \color{green}{ x = \frac{16}{19} } & & \\ & V = \left\{ \frac{16}{19} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{-9}& = & -7 \color{red}{ -4x } \\\Leftrightarrow & -x \color{red}{-9}\color{blue}{+9+4x } & = & -7 \color{red}{ -4x }\color{blue}{+9+4x } \\\Leftrightarrow & -x \color{blue}{+4x } & = & -7 \color{blue}{+9} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+15}& = & -2 \color{red}{ -11x } \\\Leftrightarrow & 3x \color{red}{+15}\color{blue}{-15+11x } & = & -2 \color{red}{ -11x }\color{blue}{-15+11x } \\\Leftrightarrow & 3x \color{blue}{+11x } & = & -2 \color{blue}{-15} \\\Leftrightarrow &14x & = &-17\\\Leftrightarrow & \color{red}{14}x & = &-17\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}{ 14}} & = & \frac{-17}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{14} } & & \\ & V = \left\{ \frac{-17}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+6}& = & 4 \color{red}{ +10x } \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6-10x } & = & 4 \color{red}{ +10x }\color{blue}{-6-10x } \\\Leftrightarrow & 13x \color{blue}{-10x } & = & 4 \color{blue}{-6} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}{ 3}} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+12}& = & -5 \color{red}{ +3x } \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12-3x } & = & -5 \color{red}{ +3x }\color{blue}{-12-3x } \\\Leftrightarrow & 4x \color{blue}{-3x } & = & -5 \color{blue}{-12} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+4}& = & 7 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4-x } & = & 7 \color{red}{ +x }\color{blue}{-4-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 7 \color{blue}{-4} \\\Leftrightarrow &-16x & = &3\\\Leftrightarrow & \color{red}{-16}x & = &3\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{3}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{16} } & & \\ & V = \left\{ \frac{-3}{16} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-10}& = & -2 \color{red}{ +14x } \\\Leftrightarrow & -11x \color{red}{-10}\color{blue}{+10-14x } & = & -2 \color{red}{ +14x }\color{blue}{+10-14x } \\\Leftrightarrow & -11x \color{blue}{-14x } & = & -2 \color{blue}{+10} \\\Leftrightarrow &-25x & = &8\\\Leftrightarrow & \color{red}{-25}x & = &8\\\Leftrightarrow & \frac{\color{red}{-25}x}{ \color{blue}{ -25}} & = & \frac{8}{-25} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{25} } & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-2}& = & -15 \color{red}{ -11x } \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2+11x } & = & -15 \color{red}{ -11x }\color{blue}{+2+11x } \\\Leftrightarrow & 15x \color{blue}{+11x } & = & -15 \color{blue}{+2} \\\Leftrightarrow &26x & = &-13\\\Leftrightarrow & \color{red}{26}x & = &-13\\\Leftrightarrow & \frac{\color{red}{26}x}{ \color{blue}{ 26}} & = & \frac{-13}{26} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+15}& = & -1 \color{red}{ +7x } \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15-7x } & = & -1 \color{red}{ +7x }\color{blue}{-15-7x } \\\Leftrightarrow & -6x \color{blue}{-7x } & = & -1 \color{blue}{-15} \\\Leftrightarrow &-13x & = &-16\\\Leftrightarrow & \color{red}{-13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}{ -13}} & = & \frac{-16}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)