Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{6} (-5x-2)& = & 3 \color{red}{-} (5+x) \\\Leftrightarrow & -30x-12& = &3-5-x \\\Leftrightarrow & -30x \color{red}{-12} & = &-2 \color{red}{-x} \\\Leftrightarrow & -30x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-2 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -30x+x& = &-2+12 \\\Leftrightarrow & -29x& = &10 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{10}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-10}{29} & & \\ & V = \left\{ \frac{-10}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-5x+2)& = & 1 \color{red}{+} (-9+3x) \\\Leftrightarrow & -20x+8& = &1-9+3x \\\Leftrightarrow & -20x \color{red}{+8} & = &-8 \color{red}{+3x} \\\Leftrightarrow & -20x \color{red}{+8} \color{blue}{-8} \color{blue}{-3x} & = &-8 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-8} \\\Leftrightarrow & -20x-3x& = &-8-8 \\\Leftrightarrow & -23x& = &-16 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-16}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{16}{23} & & \\ & V = \left\{ \frac{16}{23} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-4x-2)& = & 9 \color{red}{+} (12+3x) \\\Leftrightarrow & -16x-8& = &9+12+3x \\\Leftrightarrow & -16x \color{red}{-8} & = &21 \color{red}{+3x} \\\Leftrightarrow & -16x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &21 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & -16x-3x& = &21+8 \\\Leftrightarrow & -19x& = &29 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{29}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-29}{19} & & \\ & V = \left\{ \frac{-29}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{5} (3x-5)& = & 7 \color{red}{-} (1+x) \\\Leftrightarrow & 15x-25& = &7-1-x \\\Leftrightarrow & 15x \color{red}{-25} & = &6 \color{red}{-x} \\\Leftrightarrow & 15x \color{red}{-25} \color{blue}{+25} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+25} \\\Leftrightarrow & 15x+x& = &6+25 \\\Leftrightarrow & 16x& = &31 \\\Leftrightarrow & \frac{16x}{ \color{red}{16} }& = &\frac{31}{ \color{red}{16} } \\\Leftrightarrow & x = \frac{31}{16} & & \\ & V = \left\{ \frac{31}{16} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{3} (-4x-1)& = & -10 \color{red}{-} (10+x) \\\Leftrightarrow & -12x-3& = &-10-10-x \\\Leftrightarrow & -12x \color{red}{-3} & = &-20 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-3} \color{blue}{+3} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+3} \\\Leftrightarrow & -12x+x& = &-20+3 \\\Leftrightarrow & -11x& = &-17 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{-17}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{17}{11} & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (-4x-1)& = & 4 \color{red}{-} (8+x) \\\Leftrightarrow & -24x-6& = &4-8-x \\\Leftrightarrow & -24x \color{red}{-6} & = &-4 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &-4 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -24x+x& = &-4+6 \\\Leftrightarrow & -23x& = &2 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{2}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-2}{23} & & \\ & V = \left\{ \frac{-2}{23} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{4} (-2x-4)& = & 13 \color{red}{-} (-10+x) \\\Leftrightarrow & -8x-16& = &13+10-x \\\Leftrightarrow & -8x \color{red}{-16} & = &23 \color{red}{-x} \\\Leftrightarrow & -8x \color{red}{-16} \color{blue}{+16} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+16} \\\Leftrightarrow & -8x+x& = &23+16 \\\Leftrightarrow & -7x& = &39 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{39}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{-39}{7} & & \\ & V = \left\{ \frac{-39}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{5} (6x+7)& = & 10 \color{red}{+} (-15+x) \\\Leftrightarrow & 30x+35& = &10-15+x \\\Leftrightarrow & 30x \color{red}{+35} & = &-5 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{+35} \color{blue}{-35} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{-35} \\\Leftrightarrow & 30x-x& = &-5-35 \\\Leftrightarrow & 29x& = &-40 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-40}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-40}{29} & & \\ & V = \left\{ \frac{-40}{29} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{2} (-3x-3)& = & -4 \color{red}{-} (-3-5x) \\\Leftrightarrow & -6x-6& = &-4+3+5x \\\Leftrightarrow & -6x \color{red}{-6} & = &-1 \color{red}{+5x} \\\Leftrightarrow & -6x \color{red}{-6} \color{blue}{+6} \color{blue}{-5x} & = &-1 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+6} \\\Leftrightarrow & -6x-5x& = &-1+6 \\\Leftrightarrow & -11x& = &5 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{5}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-5}{11} & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{6} (6x+3)& = & -12 \color{red}{+} (-5+x) \\\Leftrightarrow & 36x+18& = &-12-5+x \\\Leftrightarrow & 36x \color{red}{+18} & = &-17 \color{red}{+x} \\\Leftrightarrow & 36x \color{red}{+18} \color{blue}{-18} \color{blue}{-x} & = &-17 \color{red}{+x} \color{blue}{-x} \color{blue}{-18} \\\Leftrightarrow & 36x-x& = &-17-18 \\\Leftrightarrow & 35x& = &-35 \\\Leftrightarrow & \frac{35x}{ \color{red}{35} }& = &\frac{-35}{ \color{red}{35} } \\\Leftrightarrow & x = -1 & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{6} (x+4)& = & 12 \color{red}{-} (-2+x) \\\Leftrightarrow & 6x+24& = &12+2-x \\\Leftrightarrow & 6x \color{red}{+24} & = &14 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{+24} \color{blue}{-24} \color{blue}{+x} & = &14 \color{red}{-x} \color{blue}{+x} \color{blue}{-24} \\\Leftrightarrow & 6x+x& = &14-24 \\\Leftrightarrow & 7x& = &-10 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-10}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (x-7)& = & 15 \color{red}{-} (9-3x) \\\Leftrightarrow & 4x-28& = &15-9+3x \\\Leftrightarrow & 4x \color{red}{-28} & = &6 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-28} \color{blue}{+28} \color{blue}{-3x} & = &6 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+28} \\\Leftrightarrow & 4x-3x& = &6+28 \\\Leftrightarrow & x& = &34 \\ & V = \left\{ 34 \right\} & \\\end{align}\)