Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{147x} +14 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+30} \\\Leftrightarrow & -210x-147x& = & 14+30 \\\Leftrightarrow & \color{red}{-357} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-357} & & \\\Leftrightarrow & x = \frac{-44}{357} & & \\ & V = \left\{ \frac{-44}{357} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 9x+\frac{12}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{891}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 891x \color{red}{+108} & = & \color{red}{693x} +88 \\\Leftrightarrow & 891x \color{red}{+108} \color{blue}{-108} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{-108} \\\Leftrightarrow & 891x-693x& = & 88-108 \\\Leftrightarrow & \color{red}{198} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{198} & & \\\Leftrightarrow & x = \frac{-10}{99} & & \\ & V = \left\{ \frac{-10}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+168} & = & \color{red}{-245x} +45 \\\Leftrightarrow & 1050x \color{red}{+168} \color{blue}{-168} \color{blue}{+245x} & = & \color{red}{-245x} +45 \color{blue}{+245x} \color{blue}{-168} \\\Leftrightarrow & 1050x+245x& = & 45-168 \\\Leftrightarrow & \color{red}{1295} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{1295} & & \\ & V = \left\{ \frac{-123}{1295} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{3}{5})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 6x+\frac{9}{5}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+63} & = & \color{red}{-245x} +10 \\\Leftrightarrow & 210x \color{red}{+63} \color{blue}{-63} \color{blue}{+245x} & = & \color{red}{-245x} +10 \color{blue}{+245x} \color{blue}{-63} \\\Leftrightarrow & 210x+245x& = & 10-63 \\\Leftrightarrow & \color{red}{455} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{455} & & \\ & V = \left\{ \frac{-53}{455} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{3})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 20x+\frac{25}{3}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{175}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{147x} +18 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{-147x} & = & \color{red}{147x} +18 \color{blue}{-147x} \color{blue}{-175} \\\Leftrightarrow & 420x-147x& = & 18-175 \\\Leftrightarrow & \color{red}{273} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{273} & & \\ & V = \left\{ \frac{-157}{273} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{4})& = & -6x+\frac{10}{11} \\\Leftrightarrow & 25x+\frac{15}{4}& = & -6x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-264}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{+165} & = & \color{red}{-264x} +40 \\\Leftrightarrow & 1100x \color{red}{+165} \color{blue}{-165} \color{blue}{+264x} & = & \color{red}{-264x} +40 \color{blue}{+264x} \color{blue}{-165} \\\Leftrightarrow & 1100x+264x& = & 40-165 \\\Leftrightarrow & \color{red}{1364} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1364} & & \\ & V = \left\{ \frac{-125}{1364} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{11})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{14}{11}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-154}{ \color{blue}{11} }x+ \frac{14}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -154x \color{red}{+14} & = & \color{red}{33x} +6 \\\Leftrightarrow & -154x \color{red}{+14} \color{blue}{-14} \color{blue}{-33x} & = & \color{red}{33x} +6 \color{blue}{-33x} \color{blue}{-14} \\\Leftrightarrow & -154x-33x& = & 6-14 \\\Leftrightarrow & \color{red}{-187} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-187} & & \\\Leftrightarrow & x = \frac{8}{187} & & \\ & V = \left\{ \frac{8}{187} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{3})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -14x-\frac{35}{3}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-168}{ \color{blue}{12} }x- \frac{140}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -168x \color{red}{-140} & = & \color{red}{-60x} +9 \\\Leftrightarrow & -168x \color{red}{-140} \color{blue}{+140} \color{blue}{+60x} & = & \color{red}{-60x} +9 \color{blue}{+60x} \color{blue}{+140} \\\Leftrightarrow & -168x+60x& = & 9+140 \\\Leftrightarrow & \color{red}{-108} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-108} & & \\\Leftrightarrow & x = \frac{-149}{108} & & \\ & V = \left\{ \frac{-149}{108} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{3})& = & -7x+\frac{9}{8} \\\Leftrightarrow & -16x+\frac{20}{3}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-384}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -384x \color{red}{+160} & = & \color{red}{-168x} +27 \\\Leftrightarrow & -384x \color{red}{+160} \color{blue}{-160} \color{blue}{+168x} & = & \color{red}{-168x} +27 \color{blue}{+168x} \color{blue}{-160} \\\Leftrightarrow & -384x+168x& = & 27-160 \\\Leftrightarrow & \color{red}{-216} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-216} & & \\\Leftrightarrow & x = \frac{133}{216} & & \\ & V = \left\{ \frac{133}{216} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{-54} & = & \color{red}{231x} +110 \\\Leftrightarrow & -990x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & -990x-231x& = & 110+54 \\\Leftrightarrow & \color{red}{-1221} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-1221} & & \\\Leftrightarrow & x = \frac{-164}{1221} & & \\ & V = \left\{ \frac{-164}{1221} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -30x+\frac{30}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+90} & = & \color{red}{231x} +22 \\\Leftrightarrow & -990x \color{red}{+90} \color{blue}{-90} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-90} \\\Leftrightarrow & -990x-231x& = & 22-90 \\\Leftrightarrow & \color{red}{-1221} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{-1221} & & \\\Leftrightarrow & x = \frac{68}{1221} & & \\ & V = \left\{ \frac{68}{1221} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+20} & = & \color{red}{-21x} +2 \\\Leftrightarrow & 60x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & 60x+21x& = & 2-20 \\\Leftrightarrow & \color{red}{81} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{81} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)