Vgln. eerste graad (reeks 2)

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

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

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Bepaal de waarde van x. Meerdere manieren van oplossen mogelijk

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-3}& = & 6 \color{red}{ +x } \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3-x } & = & 6 \color{red}{ +x }\color{blue}{+3-x } \\\Leftrightarrow & -15x \color{blue}{-x } & = & 6 \color{blue}{+3} \\\Leftrightarrow &-16x & = &9\\\Leftrightarrow & \color{red}{-16}x & = &9\\\Leftrightarrow & \frac{\color{red}{-16}x}{ \color{blue}{ -16}} & = & \frac{9}{-16} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{16} } & & \\ & V = \left\{ \frac{-9}{16} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+7}& = & -7 \color{red}{ -7x } \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7+7x } & = & -7 \color{red}{ -7x }\color{blue}{-7+7x } \\\Leftrightarrow & x \color{blue}{+7x } & = & -7 \color{blue}{-7} \\\Leftrightarrow &8x & = &-14\\\Leftrightarrow & \color{red}{8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{-14}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+6}& = & 10 \color{red}{ -2x } \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6+2x } & = & 10 \color{red}{ -2x }\color{blue}{-6+2x } \\\Leftrightarrow & -x \color{blue}{+2x } & = & 10 \color{blue}{-6} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+2}& = & 12 \color{red}{ -13x } \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2+13x } & = & 12 \color{red}{ -13x }\color{blue}{-2+13x } \\\Leftrightarrow & 14x \color{blue}{+13x } & = & 12 \color{blue}{-2} \\\Leftrightarrow &27x & = &10\\\Leftrightarrow & \color{red}{27}x & = &10\\\Leftrightarrow & \frac{\color{red}{27}x}{ \color{blue}{ 27}} & = & \frac{10}{27} \\\Leftrightarrow & \color{green}{ x = \frac{10}{27} } & & \\ & V = \left\{ \frac{10}{27} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-7}& = & -3 \color{red}{ +8x } \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7-8x } & = & -3 \color{red}{ +8x }\color{blue}{+7-8x } \\\Leftrightarrow & -15x \color{blue}{-8x } & = & -3 \color{blue}{+7} \\\Leftrightarrow &-23x & = &4\\\Leftrightarrow & \color{red}{-23}x & = &4\\\Leftrightarrow & \frac{\color{red}{-23}x}{ \color{blue}{ -23}} & = & \frac{4}{-23} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{23} } & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{-9}& = & -2 \color{red}{ -7x } \\\Leftrightarrow & 12x \color{red}{-9}\color{blue}{+9+7x } & = & -2 \color{red}{ -7x }\color{blue}{+9+7x } \\\Leftrightarrow & 12x \color{blue}{+7x } & = & -2 \color{blue}{+9} \\\Leftrightarrow &19x & = &7\\\Leftrightarrow & \color{red}{19}x & = &7\\\Leftrightarrow & \frac{\color{red}{19}x}{ \color{blue}{ 19}} & = & \frac{7}{19} \\\Leftrightarrow & \color{green}{ x = \frac{7}{19} } & & \\ & V = \left\{ \frac{7}{19} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-4}& = & -3 \color{red}{ -11x } \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4+11x } & = & -3 \color{red}{ -11x }\color{blue}{+4+11x } \\\Leftrightarrow & 12x \color{blue}{+11x } & = & -3 \color{blue}{+4} \\\Leftrightarrow &23x & = &1\\\Leftrightarrow & \color{red}{23}x & = &1\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{1}{23} \\\Leftrightarrow & \color{green}{ x = \frac{1}{23} } & & \\ & V = \left\{ \frac{1}{23} \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+15}& = & -8 \color{red}{ +x } \\\Leftrightarrow & 2x \color{red}{+15}\color{blue}{-15-x } & = & -8 \color{red}{ +x }\color{blue}{-15-x } \\\Leftrightarrow & 2x \color{blue}{-x } & = & -8 \color{blue}{-15} \\\Leftrightarrow &x & = &-23\\\Leftrightarrow & \color{red}{}x & = &-23\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}{ 1}} & = & -23 \\\Leftrightarrow & \color{green}{ x = -23 } & & \\ & V = \left\{ -23 \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+15}& = & 1 \color{red}{ +11x } \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15-11x } & = & 1 \color{red}{ +11x }\color{blue}{-15-11x } \\\Leftrightarrow & 4x \color{blue}{-11x } & = & 1 \color{blue}{-15} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}{ -7}} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+1}& = & 13 \color{red}{ -15x } \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1+15x } & = & 13 \color{red}{ -15x }\color{blue}{-1+15x } \\\Leftrightarrow & 8x \color{blue}{+15x } & = & 13 \color{blue}{-1} \\\Leftrightarrow &23x & = &12\\\Leftrightarrow & \color{red}{23}x & = &12\\\Leftrightarrow & \frac{\color{red}{23}x}{ \color{blue}{ 23}} & = & \frac{12}{23} \\\Leftrightarrow & \color{green}{ x = \frac{12}{23} } & & \\ & V = \left\{ \frac{12}{23} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+4}& = & 13 \color{red}{ +5x } \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4-5x } & = & 13 \color{red}{ +5x }\color{blue}{-4-5x } \\\Leftrightarrow & 13x \color{blue}{-5x } & = & 13 \color{blue}{-4} \\\Leftrightarrow &8x & = &9\\\Leftrightarrow & \color{red}{8}x & = &9\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}{ 8}} & = & \frac{9}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-9}& = & -13 \color{red}{ +4x } \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9-4x } & = & -13 \color{red}{ +4x }\color{blue}{+9-4x } \\\Leftrightarrow & -15x \color{blue}{-4x } & = & -13 \color{blue}{+9} \\\Leftrightarrow &-19x & = &-4\\\Leftrightarrow & \color{red}{-19}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-19}x}{ \color{blue}{ -19}} & = & \frac{-4}{-19} \\\Leftrightarrow & \color{green}{ x = \frac{4}{19} } & & \\ & V = \left\{ \frac{4}{19} \right\} & \\\end{align}\)