Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer  🖨

Alles samen. Gebruik stappenplan en ZRM!

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

---

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{9})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -14x-\frac{35}{9}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-35} & = & \color{red}{27x} +12 \\\Leftrightarrow & -126x \color{red}{-35} \color{blue}{+35} \color{blue}{-27x} & = & \color{red}{27x} +12 \color{blue}{-27x} \color{blue}{+35} \\\Leftrightarrow & -126x-27x& = & 12+35 \\\Leftrightarrow & \color{red}{-153} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-153} & & \\\Leftrightarrow & x = \frac{-47}{153} & & \\ & V = \left\{ \frac{-47}{153} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & -6x+\frac{3}{8} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -6x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{280}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-48}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{+21} & = & \color{red}{-48x} +3 \\\Leftrightarrow & 280x \color{red}{+21} \color{blue}{-21} \color{blue}{+48x} & = & \color{red}{-48x} +3 \color{blue}{+48x} \color{blue}{-21} \\\Leftrightarrow & 280x+48x& = & 3-21 \\\Leftrightarrow & \color{red}{328} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{328} & & \\\Leftrightarrow & x = \frac{-9}{164} & & \\ & V = \left\{ \frac{-9}{164} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{9}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{9}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-9} & = & \color{red}{35x} +8 \\\Leftrightarrow & -84x \color{red}{-9} \color{blue}{+9} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+9} \\\Leftrightarrow & -84x-35x& = & 8+9 \\\Leftrightarrow & \color{red}{-119} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-119} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{11})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 6x-\frac{6}{11}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{792}{ \color{blue}{132} }x- \frac{72}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 792x \color{red}{-72} & = & \color{red}{-924x} +77 \\\Leftrightarrow & 792x \color{red}{-72} \color{blue}{+72} \color{blue}{+924x} & = & \color{red}{-924x} +77 \color{blue}{+924x} \color{blue}{+72} \\\Leftrightarrow & 792x+924x& = & 77+72 \\\Leftrightarrow & \color{red}{1716} x& = & 149 \\\Leftrightarrow & x = \frac{149}{1716} & & \\ & V = \left\{ \frac{149}{1716} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{16}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-48} & = & \color{red}{165x} +88 \\\Leftrightarrow & -396x \color{red}{-48} \color{blue}{+48} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+48} \\\Leftrightarrow & -396x-165x& = & 88+48 \\\Leftrightarrow & \color{red}{-561} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-561} & & \\\Leftrightarrow & x = \frac{-8}{33} & & \\ & V = \left\{ \frac{-8}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{840}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{196x} +63 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{-120} \\\Leftrightarrow & 840x-196x& = & 63-120 \\\Leftrightarrow & \color{red}{644} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{644} & & \\ & V = \left\{ \frac{-57}{644} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+84} & = & \color{red}{-175x} +30 \\\Leftrightarrow & 630x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 630x+175x& = & 30-84 \\\Leftrightarrow & \color{red}{805} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{805} & & \\ & V = \left\{ \frac{-54}{805} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+150} & = & \color{red}{175x} +42 \\\Leftrightarrow & -840x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -840x-175x& = & 42-150 \\\Leftrightarrow & \color{red}{-1015} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-1015} & & \\\Leftrightarrow & x = \frac{108}{1015} & & \\ & V = \left\{ \frac{108}{1015} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{20}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+180} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{-180} \\\Leftrightarrow & 1260x+441x& = & 14-180 \\\Leftrightarrow & \color{red}{1701} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{1701} & & \\ & V = \left\{ \frac{-166}{1701} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{3})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+8} & = & \color{red}{-21x} +8 \\\Leftrightarrow & 30x \color{red}{+8} \color{blue}{-8} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-8} \\\Leftrightarrow & 30x+21x& = & 8-8 \\\Leftrightarrow & \color{red}{51} x& = & 0 \\\Leftrightarrow & x = \frac{0}{51} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{11})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{-270} & = & \color{red}{-495x} +22 \\\Leftrightarrow & 1188x \color{red}{-270} \color{blue}{+270} \color{blue}{+495x} & = & \color{red}{-495x} +22 \color{blue}{+495x} \color{blue}{+270} \\\Leftrightarrow & 1188x+495x& = & 22+270 \\\Leftrightarrow & \color{red}{1683} x& = & 292 \\\Leftrightarrow & x = \frac{292}{1683} & & \\ & V = \left\{ \frac{292}{1683} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{11})& = & 3x+\frac{3}{7} \\\Leftrightarrow & -20x+\frac{20}{11}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+140} & = & \color{red}{231x} +33 \\\Leftrightarrow & -1540x \color{red}{+140} \color{blue}{-140} \color{blue}{-231x} & = & \color{red}{231x} +33 \color{blue}{-231x} \color{blue}{-140} \\\Leftrightarrow & -1540x-231x& = & 33-140 \\\Leftrightarrow & \color{red}{-1771} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-1771} & & \\\Leftrightarrow & x = \frac{107}{1771} & & \\ & V = \left\{ \frac{107}{1771} \right\} & \\\end{align}\)