Vgln. eerste graad (reeks 3)

Hoofdmenu Eentje per keer  🖨

Reeks met haakjes

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

---

Reeks met haakjes

Verbetersleutel

1. \(\begin{align} & \color{red}{5} (-5x-1)& = & -4 \color{red}{-} (-3-4x) \\\Leftrightarrow & -25x-5& = &-4+3+4x \\\Leftrightarrow & -25x \color{red}{-5} & = &-1 \color{red}{+4x} \\\Leftrightarrow & -25x \color{red}{-5} \color{blue}{+5} \color{blue}{-4x} & = &-1 \color{red}{+4x} \color{blue}{-4x} \color{blue}{+5} \\\Leftrightarrow & -25x-4x& = &-1+5 \\\Leftrightarrow & -29x& = &4 \\\Leftrightarrow & \frac{-29x}{ \color{red}{-29} }& = &\frac{4}{ \color{red}{-29} } \\\Leftrightarrow & x = \frac{-4}{29} & & \\ & V = \left\{ \frac{-4}{29} \right\} & \\\end{align}\)
2. \(\begin{align} & \color{red}{4} (-2x-1)& = & 3 \color{red}{-} (-9-5x) \\\Leftrightarrow & -8x-4& = &3+9+5x \\\Leftrightarrow & -8x \color{red}{-4} & = &12 \color{red}{+5x} \\\Leftrightarrow & -8x \color{red}{-4} \color{blue}{+4} \color{blue}{-5x} & = &12 \color{red}{+5x} \color{blue}{-5x} \color{blue}{+4} \\\Leftrightarrow & -8x-5x& = &12+4 \\\Leftrightarrow & -13x& = &16 \\\Leftrightarrow & \frac{-13x}{ \color{red}{-13} }& = &\frac{16}{ \color{red}{-13} } \\\Leftrightarrow & x = \frac{-16}{13} & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & \color{red}{5} (3x+2)& = & 15 \color{red}{-} (-3+4x) \\\Leftrightarrow & 15x+10& = &15+3-4x \\\Leftrightarrow & 15x \color{red}{+10} & = &18 \color{red}{-4x} \\\Leftrightarrow & 15x \color{red}{+10} \color{blue}{-10} \color{blue}{+4x} & = &18 \color{red}{-4x} \color{blue}{+4x} \color{blue}{-10} \\\Leftrightarrow & 15x+4x& = &18-10 \\\Leftrightarrow & 19x& = &8 \\\Leftrightarrow & \frac{19x}{ \color{red}{19} }& = &\frac{8}{ \color{red}{19} } \\\Leftrightarrow & x = \frac{8}{19} & & \\ & V = \left\{ \frac{8}{19} \right\} & \\\end{align}\)
4. \(\begin{align} & \color{red}{3} (2x-5)& = & -7 \color{red}{-} (-14+x) \\\Leftrightarrow & 6x-15& = &-7+14-x \\\Leftrightarrow & 6x \color{red}{-15} & = &7 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-15} \color{blue}{+15} \color{blue}{+x} & = &7 \color{red}{-x} \color{blue}{+x} \color{blue}{+15} \\\Leftrightarrow & 6x+x& = &7+15 \\\Leftrightarrow & 7x& = &22 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{22}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{22}{7} & & \\ & V = \left\{ \frac{22}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & \color{red}{2} (-5x+3)& = & 12 \color{red}{+} (-14-3x) \\\Leftrightarrow & -10x+6& = &12-14-3x \\\Leftrightarrow & -10x \color{red}{+6} & = &-2 \color{red}{-3x} \\\Leftrightarrow & -10x \color{red}{+6} \color{blue}{-6} \color{blue}{+3x} & = &-2 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-6} \\\Leftrightarrow & -10x+3x& = &-2-6 \\\Leftrightarrow & -7x& = &-8 \\\Leftrightarrow & \frac{-7x}{ \color{red}{-7} }& = &\frac{-8}{ \color{red}{-7} } \\\Leftrightarrow & x = \frac{8}{7} & & \\ & V = \left\{ \frac{8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & \color{red}{5} (5x+5)& = & -7 \color{red}{+} (9+x) \\\Leftrightarrow & 25x+25& = &-7+9+x \\\Leftrightarrow & 25x \color{red}{+25} & = &2 \color{red}{+x} \\\Leftrightarrow & 25x \color{red}{+25} \color{blue}{-25} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-25} \\\Leftrightarrow & 25x-x& = &2-25 \\\Leftrightarrow & 24x& = &-23 \\\Leftrightarrow & \frac{24x}{ \color{red}{24} }& = &\frac{-23}{ \color{red}{24} } \\\Leftrightarrow & x = \frac{-23}{24} & & \\ & V = \left\{ \frac{-23}{24} \right\} & \\\end{align}\)
7. \(\begin{align} & \color{red}{6} (4x-2)& = & -14 \color{red}{-} (6+x) \\\Leftrightarrow & 24x-12& = &-14-6-x \\\Leftrightarrow & 24x \color{red}{-12} & = &-20 \color{red}{-x} \\\Leftrightarrow & 24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-20 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & 24x+x& = &-20+12 \\\Leftrightarrow & 25x& = &-8 \\\Leftrightarrow & \frac{25x}{ \color{red}{25} }& = &\frac{-8}{ \color{red}{25} } \\\Leftrightarrow & x = \frac{-8}{25} & & \\ & V = \left\{ \frac{-8}{25} \right\} & \\\end{align}\)
8. \(\begin{align} & \color{red}{6} (-4x-2)& = & -15 \color{red}{-} (-10+x) \\\Leftrightarrow & -24x-12& = &-15+10-x \\\Leftrightarrow & -24x \color{red}{-12} & = &-5 \color{red}{-x} \\\Leftrightarrow & -24x \color{red}{-12} \color{blue}{+12} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{+12} \\\Leftrightarrow & -24x+x& = &-5+12 \\\Leftrightarrow & -23x& = &7 \\\Leftrightarrow & \frac{-23x}{ \color{red}{-23} }& = &\frac{7}{ \color{red}{-23} } \\\Leftrightarrow & x = \frac{-7}{23} & & \\ & V = \left\{ \frac{-7}{23} \right\} & \\\end{align}\)
9. \(\begin{align} & \color{red}{3} (x+7)& = & -4 \color{red}{-} (1+x) \\\Leftrightarrow & 3x+21& = &-4-1-x \\\Leftrightarrow & 3x \color{red}{+21} & = &-5 \color{red}{-x} \\\Leftrightarrow & 3x \color{red}{+21} \color{blue}{-21} \color{blue}{+x} & = &-5 \color{red}{-x} \color{blue}{+x} \color{blue}{-21} \\\Leftrightarrow & 3x+x& = &-5-21 \\\Leftrightarrow & 4x& = &-26 \\\Leftrightarrow & \frac{4x}{ \color{red}{4} }& = &\frac{-26}{ \color{red}{4} } \\\Leftrightarrow & x = \frac{-13}{2} & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & \color{red}{5} (2x+1)& = & -12 \color{red}{+} (-14-3x) \\\Leftrightarrow & 10x+5& = &-12-14-3x \\\Leftrightarrow & 10x \color{red}{+5} & = &-26 \color{red}{-3x} \\\Leftrightarrow & 10x \color{red}{+5} \color{blue}{-5} \color{blue}{+3x} & = &-26 \color{red}{-3x} \color{blue}{+3x} \color{blue}{-5} \\\Leftrightarrow & 10x+3x& = &-26-5 \\\Leftrightarrow & 13x& = &-31 \\\Leftrightarrow & \frac{13x}{ \color{red}{13} }& = &\frac{-31}{ \color{red}{13} } \\\Leftrightarrow & x = \frac{-31}{13} & & \\ & V = \left\{ \frac{-31}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & \color{red}{2} (3x-2)& = & 15 \color{red}{-} (-8+x) \\\Leftrightarrow & 6x-4& = &15+8-x \\\Leftrightarrow & 6x \color{red}{-4} & = &23 \color{red}{-x} \\\Leftrightarrow & 6x \color{red}{-4} \color{blue}{+4} \color{blue}{+x} & = &23 \color{red}{-x} \color{blue}{+x} \color{blue}{+4} \\\Leftrightarrow & 6x+x& = &23+4 \\\Leftrightarrow & 7x& = &27 \\\Leftrightarrow & \frac{7x}{ \color{red}{7} }& = &\frac{27}{ \color{red}{7} } \\\Leftrightarrow & x = \frac{27}{7} & & \\ & V = \left\{ \frac{27}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & \color{red}{6} (4x+5)& = & -2 \color{red}{+} (4+x) \\\Leftrightarrow & 24x+30& = &-2+4+x \\\Leftrightarrow & 24x \color{red}{+30} & = &2 \color{red}{+x} \\\Leftrightarrow & 24x \color{red}{+30} \color{blue}{-30} \color{blue}{-x} & = &2 \color{red}{+x} \color{blue}{-x} \color{blue}{-30} \\\Leftrightarrow & 24x-x& = &2-30 \\\Leftrightarrow & 23x& = &-28 \\\Leftrightarrow & \frac{23x}{ \color{red}{23} }& = &\frac{-28}{ \color{red}{23} } \\\Leftrightarrow & x = \frac{-28}{23} & & \\ & V = \left\{ \frac{-28}{23} \right\} & \\\end{align}\)