Vgln. eerste graad (reeks 3)

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Reeks met haakjes

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

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Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{3} (3x-4)& = & 15 \color{red}{-} (-15-4x) \\\Leftrightarrow & 9x-12& = &15+15+4x \\\Leftrightarrow & 9x \color{red}{-12} & = &30 \color{red}{+4x} \\\Leftrightarrow & 9x \color{red}{-12} \color{blue}{+12} \color{blue}{-4x} & = &30 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+12} \\\Leftrightarrow & 9x-4x& = &30+12 \\\Leftrightarrow & 5x& = &42 \\\Leftrightarrow & \frac{5x}{ \color{red}{5} }& = &\frac{42}{ \color{red}{5} } \\\Leftrightarrow & x = \frac{42}{5} & & \\ & V = \left\{ \frac{42}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{3} (-2x+6)& = & 14 \color{red}{-} (1+x) \\\Leftrightarrow & -6x+18& = &14-1-x \\\Leftrightarrow & -6x \color{red}{+18} & = &13 \color{red}{-x} \\\Leftrightarrow & -6x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & -6x+x& = &13-18 \\\Leftrightarrow & -5x& = &-5 \\\Leftrightarrow & \frac{-5x}{ \color{red}{-5} }& = &\frac{-5}{ \color{red}{-5} } \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{2} (-6x-6)& = & -12 \color{red}{-} (-3+x) \\\Leftrightarrow & -12x-12& = &-12+3-x \\\Leftrightarrow & -12x \color{red}{-12} & = &-9 \color{red}{-x} \\\Leftrightarrow & -12x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-9 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -12x+x& = &-9+12 \\\Leftrightarrow & -11x& = &3 \\\Leftrightarrow & \frac{-11x}{ \color{red}{-11} }& = &\frac{3}{ \color{red}{-11} } \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{4} (-4x-4)& = & -11 \color{red}{+} (-5+x) \\\Leftrightarrow & -16x-16& = &-11-5+x \\\Leftrightarrow & -16x \color{red}{-16} & = &-16 \color{red}{+x} \\\Leftrightarrow & -16x \color{red}{-16} \color{blue}{+16} \color{blue}{-x} & = &-16 \color{red}{+x} \color{blue}{-x} \color{blue}{+16} \\\Leftrightarrow & -16x-x& = &-16+16 \\\Leftrightarrow & -17x& = &0 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{0}{ \color{red}{-17} } \\\Leftrightarrow & x = 0 & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (2x-4)& = & 11 \color{red}{+} (15+3x) \\\Leftrightarrow & 4x-8& = &11+15+3x \\\Leftrightarrow & 4x \color{red}{-8} & = &26 \color{red}{+3x} \\\Leftrightarrow & 4x \color{red}{-8} \color{blue}{+8} \color{blue}{-3x} & = &26 \color{red}{+3x} \color{blue}{-3x} \color{blue}{+8} \\\Leftrightarrow & 4x-3x& = &26+8 \\\Leftrightarrow & x& = &34 \\ & V = \left\{ 34 \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{6} (4x+3)& = & 9 \color{red}{-} (8+x) \\\Leftrightarrow & 24x+18& = &9-8-x \\\Leftrightarrow & 24x \color{red}{+18} & = &1 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{+18} \color{blue}{-18} \color{blue}{+x} & = &1 \color{red}{-x} \color{blue}{+x} \color{blue}{-18} \\\Leftrightarrow & 24x+x& = &1-18 \\\Leftrightarrow & 25x& = &-17 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-17}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-17}{25} & & \\ & V = \left\{ \frac{-17}{25} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{5} (-3x-7)& = & -15 \color{red}{-} (7-2x) \\\Leftrightarrow & -15x-35& = &-15-7+2x \\\Leftrightarrow & -15x \color{red}{-35} & = &-22 \color{red}{+2x} \\\Leftrightarrow & -15x \color{red}{-35} \color{blue}{+35} \color{blue}{-2x} & = &-22 \color{red}{+2x} \color{blue}{-2x} \color{blue}{+35} \\\Leftrightarrow & -15x-2x& = &-22+35 \\\Leftrightarrow & -17x& = &13 \\\Leftrightarrow & \frac{-17x}{ \color{red}{-17} }& = &\frac{13}{ \color{red}{-17} } \\\Leftrightarrow & x = \frac{-13}{17} & & \\ & V = \left\{ \frac{-13}{17} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{2} (5x+5)& = & 13 \color{red}{-} (-1-3x) \\\Leftrightarrow & 10x+10& = &13+1+3x \\\Leftrightarrow & 10x \color{red}{+10} & = &14 \color{red}{+3x} \\\Leftrightarrow & 10x \color{red}{+10} \color{blue}{-10} \color{blue}{-3x} & = &14 \color{red}{+3x} \color{blue}{-3x} \color{blue}{-10} \\\Leftrightarrow & 10x-3x& = &14-10 \\\Leftrightarrow & 7x& = &4 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{4}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{4} (4x-6)& = & 5 \color{red}{-} (-15+x) \\\Leftrightarrow & 16x-24& = &5+15-x \\\Leftrightarrow & 16x \color{red}{-24} & = &20 \color{red}{-x} \\\Leftrightarrow & 16x \color{red}{-24} \color{blue}{+24} \color{blue}{+x} & = &20 \color{red}{-x} \color{blue}{+x} \color{blue}{+24} \\\Leftrightarrow & 16x+x& = &20+24 \\\Leftrightarrow & 17x& = &44 \\\Leftrightarrow & \frac{17x}{ \color{red}{17} }& = &\frac{44}{ \color{red}{17} } \\\Leftrightarrow & x = \frac{44}{17} & & \\ & V = \left\{ \frac{44}{17} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (-4x-6)& = & 3 \color{red}{-} (-10+x) \\\Leftrightarrow & -20x-30& = &3+10-x \\\Leftrightarrow & -20x \color{red}{-30} & = &13 \color{red}{-x} \\\Leftrightarrow & -20x \color{red}{-30} \color{blue}{+30} \color{blue}{+x} & = &13 \color{red}{-x} \color{blue}{+x} \color{blue}{+30} \\\Leftrightarrow & -20x+x& = &13+30 \\\Leftrightarrow & -19x& = &43 \\\Leftrightarrow & \frac{-19x}{ \color{red}{-19} }& = &\frac{43}{ \color{red}{-19} } \\\Leftrightarrow & x = \frac{-43}{19} & & \\ & V = \left\{ \frac{-43}{19} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (-2x-3)& = & -7 \color{red}{-} (-13+x) \\\Leftrightarrow & -4x-6& = &-7+13-x \\\Leftrightarrow & -4x \color{red}{-6} & = &6 \color{red}{-x} \\\Leftrightarrow & -4x \color{red}{-6} \color{blue}{+6} \color{blue}{+x} & = &6 \color{red}{-x} \color{blue}{+x} \color{blue}{+6} \\\Leftrightarrow & -4x+x& = &6+6 \\\Leftrightarrow & -3x& = &12 \\\Leftrightarrow & \frac{-3x}{ \color{red}{-3} }& = &\frac{12}{ \color{red}{-3} } \\\Leftrightarrow & x = -4 & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{4} (-6x-1)& = & -10 \color{red}{-} (12+x) \\\Leftrightarrow & -24x-4& = &-10-12-x \\\Leftrightarrow & -24x \color{red}{-4} & = &-22 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &-22 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & -24x+x& = &-22+4 \\\Leftrightarrow & -23x& = &-18 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{-18}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{18}{23} & & \\ & V = \left\{ \frac{18}{23} \right\} & \\\end{align}\)