Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+84} & = & \color{red}{175x} +20 \\\Leftrightarrow & 630x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 630x-175x& = & 20-84 \\\Leftrightarrow & \color{red}{455} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{455} & & \\ & V = \left\{ \frac{-64}{455} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{63x} +24 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +24 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -90x-63x& = & 24+8 \\\Leftrightarrow & \color{red}{-153} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-153} & & \\\Leftrightarrow & x = \frac{-32}{153} & & \\ & V = \left\{ \frac{-32}{153} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{9})& = & 3x+\frac{5}{6} \\\Leftrightarrow & -35x+\frac{35}{9}& = & 3x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x+ \frac{70}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{+70} & = & \color{red}{54x} +15 \\\Leftrightarrow & -630x \color{red}{+70} \color{blue}{-70} \color{blue}{-54x} & = & \color{red}{54x} +15 \color{blue}{-54x} \color{blue}{-70} \\\Leftrightarrow & -630x-54x& = & 15-70 \\\Leftrightarrow & \color{red}{-684} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-684} & & \\\Leftrightarrow & x = \frac{55}{684} & & \\ & V = \left\{ \frac{55}{684} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{4})& = & 4x+\frac{5}{6} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 4x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{48x} +10 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{-48x} & = & \color{red}{48x} +10 \color{blue}{-48x} \color{blue}{-45} \\\Leftrightarrow & -180x-48x& = & 10-45 \\\Leftrightarrow & \color{red}{-228} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-228} & & \\\Leftrightarrow & x = \frac{35}{228} & & \\ & V = \left\{ \frac{35}{228} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{11})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 16x-\frac{20}{11}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{140}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-140} & = & \color{red}{-231x} +110 \\\Leftrightarrow & 1232x \color{red}{-140} \color{blue}{+140} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+140} \\\Leftrightarrow & 1232x+231x& = & 110+140 \\\Leftrightarrow & \color{red}{1463} x& = & 250 \\\Leftrightarrow & x = \frac{250}{1463} & & \\ & V = \left\{ \frac{250}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{5})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 30x+\frac{18}{5}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+126} & = & \color{red}{-245x} +20 \\\Leftrightarrow & 1050x \color{red}{+126} \color{blue}{-126} \color{blue}{+245x} & = & \color{red}{-245x} +20 \color{blue}{+245x} \color{blue}{-126} \\\Leftrightarrow & 1050x+245x& = & 20-126 \\\Leftrightarrow & \color{red}{1295} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{1295} & & \\ & V = \left\{ \frac{-106}{1295} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & -7x+\frac{2}{7} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-42} & = & \color{red}{-539x} +22 \\\Leftrightarrow & -462x \color{red}{-42} \color{blue}{+42} \color{blue}{+539x} & = & \color{red}{-539x} +22 \color{blue}{+539x} \color{blue}{+42} \\\Leftrightarrow & -462x+539x& = & 22+42 \\\Leftrightarrow & \color{red}{77} x& = & 64 \\\Leftrightarrow & x = \frac{64}{77} & & \\ & V = \left\{ \frac{64}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{7})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 30x-\frac{30}{7}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1680}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1680x \color{red}{-240} & = & \color{red}{392x} +21 \\\Leftrightarrow & 1680x \color{red}{-240} \color{blue}{+240} \color{blue}{-392x} & = & \color{red}{392x} +21 \color{blue}{-392x} \color{blue}{+240} \\\Leftrightarrow & 1680x-392x& = & 21+240 \\\Leftrightarrow & \color{red}{1288} x& = & 261 \\\Leftrightarrow & x = \frac{261}{1288} & & \\ & V = \left\{ \frac{261}{1288} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-330} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 1386x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & 1386x+385x& = & 14+330 \\\Leftrightarrow & \color{red}{1771} x& = & 344 \\\Leftrightarrow & x = \frac{344}{1771} & & \\ & V = \left\{ \frac{344}{1771} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+168} & = & \color{red}{175x} +20 \\\Leftrightarrow & -840x \color{red}{+168} \color{blue}{-168} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{-168} \\\Leftrightarrow & -840x-175x& = & 20-168 \\\Leftrightarrow & \color{red}{-1015} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{-1015} & & \\\Leftrightarrow & x = \frac{148}{1015} & & \\ & V = \left\{ \frac{148}{1015} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+264} & = & \color{red}{275x} +25 \\\Leftrightarrow & -1320x \color{red}{+264} \color{blue}{-264} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-264} \\\Leftrightarrow & -1320x-275x& = & 25-264 \\\Leftrightarrow & \color{red}{-1595} x& = & -239 \\\Leftrightarrow & x = \frac{-239}{-1595} & & \\\Leftrightarrow & x = \frac{239}{1595} & & \\ & V = \left\{ \frac{239}{1595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{12}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-84} & = & \color{red}{539x} +110 \\\Leftrightarrow & 924x \color{red}{-84} \color{blue}{+84} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{+84} \\\Leftrightarrow & 924x-539x& = & 110+84 \\\Leftrightarrow & \color{red}{385} x& = & 194 \\\Leftrightarrow & x = \frac{194}{385} & & \\ & V = \left\{ \frac{194}{385} \right\} & \\\end{align}\)