Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{4} (x+3)& = & -7 \color{red}{+} (-4-3x) \\\Leftrightarrow & 4x+12& = &-7-4-3x \\\Leftrightarrow & 4x \color{red}{+12} & = &-11 \color{red}{-3x} \\\Leftrightarrow & 4x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &-11 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 4x+3x& = &-11-12 \\\Leftrightarrow & 7x& = &-23 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{-23}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{-23}{7} & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{5} (-6x+5)& = & 6 \color{red}{+} (9+x) \\\Leftrightarrow & -30x+25& = &6+9+x \\\Leftrightarrow & -30x \color{red}{+25} & = &15 \color{red}{+x} \\\Leftrightarrow & -30x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &15 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & -30x-x& = &15-25 \\\Leftrightarrow & -31x& = &-10 \\\Leftrightarrow & \frac{-31x}{ \color{red}{-31} }& = &\frac{-10}{ \color{red}{-31} } \\\Leftrightarrow & x = \frac{10}{31} & & \\ & V = \left\{ \frac{10}{31} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{4} (-6x+5)& = & 4 \color{red}{-} (10+x) \\\Leftrightarrow & -24x+20& = &4-10-x \\\Leftrightarrow & -24x \color{red}{+20} & = &-6 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{+x} & = &-6 \color{red}{-x} \color{blue}{+x} \color{blue}{-20} \\\Leftrightarrow & -24x+x& = &-6-20 \\\Leftrightarrow & -23x& = &-26 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-26}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{26}{23} & & \\ & V = \left\{ \frac{26}{23} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (-5x+1)& = & 11 \color{red}{+} (-15-2x) \\\Leftrightarrow & -15x+3& = &11-15-2x \\\Leftrightarrow & -15x \color{red}{+3} & = &-4 \color{red}{-2x} \\\Leftrightarrow & -15x \color{red}{+3} \color{blue}{-3} \color{blue}{+2x} & = &-4 \color{red}{-2x} \color{blue}{+2x} \color{blue}{-3} \\\Leftrightarrow & -15x+2x& = &-4-3 \\\Leftrightarrow & -13x& = &-7 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{-7}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{7}{13} & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{6} (-4x-2)& = & -8 \color{red}{+} (3+x) \\\Leftrightarrow & -24x-12& = &-8+3+x \\\Leftrightarrow & -24x \color{red}{-12} & = &-5 \color{red}{+x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{-x} & = &-5 \color{red}{+x} \color{blue}{-x} \color{blue}{+12} \\\Leftrightarrow & -24x-x& = &-5+12 \\\Leftrightarrow & -25x& = &7 \\\Leftrightarrow & \frac{-25x}{ \color{red}{-25} }& = &\frac{7}{ \color{red}{-25} } \\\Leftrightarrow & x = \frac{-7}{25} & & \\ & V = \left\{ \frac{-7}{25} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{2} (5x+6)& = & 12 \color{red}{+} (13-3x) \\\Leftrightarrow & 10x+12& = &12+13-3x \\\Leftrightarrow & 10x \color{red}{+12} & = &25 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+12} \color{blue}{-12} \color{blue}{+3x} & = &25 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-12} \\\Leftrightarrow & 10x+3x& = &25-12 \\\Leftrightarrow & 13x& = &13 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{13}{ \color{red}{13} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{2} (4x+5)& = & -10 \color{red}{-} (12+x) \\\Leftrightarrow & 8x+10& = &-10-12-x \\\Leftrightarrow & 8x \color{red}{+10} & = &-22 \color{red}{-x} \\\Leftrightarrow & 8x \color{red}{+10} \color{blue}{-10} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{-10} \\\Leftrightarrow & 8x+x& = &-22-10 \\\Leftrightarrow & 9x& = &-32 \\\Leftrightarrow & \frac{9x}{ \color{red}{9} }& = &\frac{-32}{ \color{red}{9} } \\\Leftrightarrow & x = \frac{-32}{9} & & \\ & V = \left\{ \frac{-32}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-x-4)& = & -3 \color{red}{+} (1-5x) \\\Leftrightarrow & -6x-24& = &-3+1-5x \\\Leftrightarrow & -6x \color{red}{-24} & = &-2 \color{red}{-5x} \\\Leftrightarrow & -6x \color{red}{-24} \color{blue}{+24} \color{blue}{+5x} & = &-2 \color{red}{-5x} \color{blue}{+5x} \color{blue}{+24} \\\Leftrightarrow & -6x+5x& = &-2+24 \\\Leftrightarrow & -x& = &22 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{22}{ \color{red}{-1} } \\\Leftrightarrow & x = -22 & & \\ & V = \left\{ -22 \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (-x-7)& = & 7 \color{red}{-} (-7+3x) \\\Leftrightarrow & -4x-28& = &7+7-3x \\\Leftrightarrow & -4x \color{red}{-28} & = &14 \color{red}{-3x} \\\Leftrightarrow & -4x \color{red}{-28} \color{blue}{+28} \color{blue}{+3x} & = &14 \color{red}{-3x} \color{blue}{+3x} \color{blue}{+28} \\\Leftrightarrow & -4x+3x& = &14+28 \\\Leftrightarrow & -x& = &42 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{42}{ \color{red}{-1} } \\\Leftrightarrow & x = -42 & & \\ & V = \left\{ -42 \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{2} (-x+7)& = & 7 \color{red}{-} (-5+x) \\\Leftrightarrow & -2x+14& = &7+5-x \\\Leftrightarrow & -2x \color{red}{+14} & = &12 \color{red}{-x} \\\Leftrightarrow & -2x \color{red}{+14} \color{blue}{-14} \color{blue}{+x} & = &12 \color{red}{-x} \color{blue}{+x} \color{blue}{-14} \\\Leftrightarrow & -2x+x& = &12-14 \\\Leftrightarrow & -x& = &-2 \\\Leftrightarrow & \frac{-x}{ \color{red}{-1} }& = &\frac{-2}{ \color{red}{-1} } \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x+7)& = & -9 \color{red}{+} (-9+x) \\\Leftrightarrow & -4x+14& = &-9-9+x \\\Leftrightarrow & -4x \color{red}{+14} & = &-18 \color{red}{+x} \\\Leftrightarrow & -4x \color{red}{+14} \color{blue}{-14} \color{blue}{-x} & = &-18 \color{red}{+x} \color{blue}{-x} \color{blue}{-14} \\\Leftrightarrow & -4x-x& = &-18-14 \\\Leftrightarrow & -5x& = &-32 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-32}{ \color{red}{-5} } \\\Leftrightarrow & x = \frac{32}{5} & & \\ & V = \left\{ \frac{32}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{5} (6x-1)& = & -7 \color{red}{+} (-1+x) \\\Leftrightarrow & 30x-5& = &-7-1+x \\\Leftrightarrow & 30x \color{red}{-5} & = &-8 \color{red}{+x} \\\Leftrightarrow & 30x \color{red}{-5} \color{blue}{+5} \color{blue}{-x} & = &-8 \color{red}{+x} \color{blue}{-x} \color{blue}{+5} \\\Leftrightarrow & 30x-x& = &-8+5 \\\Leftrightarrow & 29x& = &-3 \\\Leftrightarrow & \frac{29x}{ \color{red}{29} }& = &\frac{-3}{ \color{red}{29} } \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)